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All Textbook Solutions for Precalculus
For Exercises 103-106, evaluate the expressions. log4log164a. Evaluate log22+log24 b. Evaluate log224 c. How do the values of the expressions in parts (a) and (b) compare?a. Evaluate log33+log327 b. Evaluate log3327 c. How do the values of the expressions in parts (a) and (b) compare?a. Evaluate log464log44 b. Evaluate log4644 c. How do the values of the expressions in parts (a) and (b) compare?a. Evaluate log100,000log100 b. Evaluate log100,000100 c. How do the values of the expressions in parts (a) and (b) compare?a. Evaluate log225 b. Evaluate 5log22 c. How do the values of the expressions in parts (a) and (b) compare?a. Evaluate log776 b. Evaluate 6log77 c. How do the values of the expressions in parts (a) and (b) compare?a. The time t (in years) required for an investment to double with interest compounded continuously depends on the interest rate r according to the function tr=ln2r. b. If an interest rate of 3.5 is secured, determine the length of time needed for an initial investment to double. Round to 1 decimal place. c. Evaluate t0.04,t0.06,andt0.08.a. The number n of monthly payments of P dollars each required to pay off a loan of A dollars in its entirety at interest rate r is given by n=log1Ar12Plog1+r12 b. college student wants to buy a car and realizes that he can only afford payments of $200 per month. If he borrows $3000 and pays it off at 6 interest, how many months will it take him to retire the loan? Round to the nearest month. c. Determine the number of monthly payments of $611.09 that would be required to pay off a home loan of $128,000 at 4 interest.For Exercises 115-116, use a calculator to approximate the given logarithms to 4 decimal places. a. Avogadro’s number is 6.0221023. Approximate log(6.0221023). b. Planck’s constant is 6.6261034Jsec. Approximate log(6.6261034). c. Compare the value of the common logarithm to the power of 10 used in scientific notation.For Exercises 115-116, use a calculator to approximate the given logarithms to 4 decimal places. a. The speed of light is 2.9979108m/sec. Approximate log (2.9979108). b. An elementary charge is 1.6021019C. Approximate log(1.6021019). c. Compare the value of the common logarithm to the power of 10 used in scientific notation.117PE118PE119PE120PE121PE122PE123PE124PE125PE126PE1PREFor Exercises 1-14, a. Write the domain. b. Write the range. c. Find the x-intercepts. d. Find the y-intercept. e. Determine the asymptotes if applicable. f. Determine the intervals over which the function is increasing. g. Determine the intervals over which the function is decreasing. h. Match the function with its graph. g(x)=2x3For Exercises 1-14, a. Write the domain. b. Write the range. c. Find the x-intercepts. d. Find the y-intercept. e. Determine the asymptotes if applicable. f. Determine the intervals over which the function is increasing. g. Determine the intervals over which the function is decreasing. h. Match the function with its graph. d(x)=(x3)24For Exercises 1-14, a. Write the domain. b. Write the range. c. Find the x-intercepts. d. Find the y-intercept. e. Determine the asymptotes if applicable. f. Determine the intervals over which the function is increasing. g. Determine the intervals over which the function is decreasing. h. Match the function with its graph. h(x)=x23For Exercises 1-14, a. Write the domain. b. Write the range. c. Find the x-intercepts. d. Find the y-intercept. e. Determine the asymptotes if applicable. f. Determine the intervals over which the function is increasing. g. Determine the intervals over which the function is decreasing. h. Match the function with its graph. k(x)=2x1For Exercises 1-14, a. Write the domain. b. Write the range. c. Find the x-intercepts. d. Find the y-intercept. e. Determine the asymptotes if applicable. f. Determine the intervals over which the function is increasing. g. Determine the intervals over which the function is decreasing. h. Match the function with its graph. zx=3xx+2For Exercises 1-14, a. Write the domain. b. Write the range. c. Find the x-intercepts. d. Find the y-intercept. e. Determine the asymptotes if applicable. f. Determine the intervals over which the function is increasing. g. Determine the intervals over which the function is decreasing. h. Match the function with its graph. px=43xFor Exercises 1-14, a. Write the domain. b. Write the range. c. Find the x-intercepts. d. Find the y-intercept. e. Determine the asymptotes if applicable. f. Determine the intervals over which the function is increasing. g. Determine the intervals over which the function is decreasing. h. Match the function with its graph. qx=x26x9For Exercises 1-14, a. Write the domain. b. Write the range. c. Find the x-intercepts. d. Find the y-intercept. e. Determine the asymptotes if applicable. f. Determine the intervals over which the function is increasing. g. Determine the intervals over which the function is decreasing. h. Match the function with its graph. mx=x41For Exercises 1-14, a. Write the domain. b. Write the range. c. Find the x-intercepts. d. Find the y-intercept. e. Determine the asymptotes if applicable. f. Determine the intervals over which the function is increasing. g. Determine the intervals over which the function is decreasing. h. Match the function with its graph. nx=x+3For Exercises 1-14, a. Write the domain. b. Write the range. c. Find the x-intercepts. d. Find the y-intercept. e. Determine the asymptotes if applicable. f. Determine the intervals over which the function is increasing. g. Determine the intervals over which the function is decreasing. h. Match the function with its graph. rx=3xFor Exercises 1-14, a. Write the domain. b. Write the range. c. Find the x-intercepts. d. Find the y-intercept. e. Determine the asymptotes if applicable. f. Determine the intervals over which the function is increasing. g. Determine the intervals over which the function is decreasing. h. Match the function with its graph. sx=x3For Exercises 1-14, a. Write the domain. b. Write the range. c. Find the x-intercepts. d. Find the y-intercept. e. Determine the asymptotes if applicable. f. Determine the intervals over which the function is increasing. g. Determine the intervals over which the function is decreasing. h. Match the function with its graph. tx=ex+2For Exercises 1-14, a. Write the domain. b. Write the range. c. Find the x-intercepts. d. Find the y-intercept. e. Determine the asymptotes if applicable. f. Determine the intervals over which the function is increasing. g. Determine the intervals over which the function is decreasing. h. Match the function with its graph. vx=lnx+2Write the logarithm as a sum and simplify if possible. Assume that a,c,andd represent positive real numbers. a.log416ab.log12cdWrite the logarithm as the difference of logarithms and simplify if possible. Assume that t represents a positive real number. a.log68tb.lne12Apply the power property of logarithms. a.log5x45b.lnx4Write the expression as the sum or difference of logarithms. a.lna4bc9b.log525a2+b23Write the expression as a single logarithm and simplify the result if possible. log354+log310log320Write the expression as a single logarithm and simplify the result if possible. a.3logx13logy23logzb.13lnt+lnt29lnt3Given that logb20.356andlogb30.565, approximate the value of logb24.a. Estimate log623 between two consecutive integers. b. Use the change-of-base formula to evaluate log623 by using base 10. Round to 4 decimal places. c. Use the change-of-base formula to evaluate log623 by using base e. Round to 4 decimal places. d. Check the result by using the related exponential form.The product property of logarithms states that logb(xy)= for positive real numbers b,x,andy,whereb1.The property of logarithms states that logbxy= for positive real numbers b,x,andy,whereb1.The power property of logarithms states that for any real number p,logbxp= for positive real numbers b,x,andy,whereb1.The change-of-base formula states that logbx can be written as a ratio of logarithms with base a as logbx=The change-of-base formula is often used to convert a logarithm to a ratio of logarithms with base or base so that a calculator can be used to approximate the logarithm.To use a graphing utility to graph the function defined by y=log5x, use the change-of-base formula to write the function as y=ory=.7PEFor Exercises 7-12, use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. (See Example 1) log749kFor Exercises 7-12, use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. (See Example 1) log8cdFor Exercises 7-12, use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. (See Example 1) log24vwFor Exercises 7-12, use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. (See Example 1) log2x+yzFor Exercises 7-12, use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. (See Example 1) log3a+bcFor Exercises 13-18, use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. (See Example 2) log12pqFor Exercises 13-18, use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. (See Example 2) log9mnFor Exercises 13-18, use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. (See Example 2) lne5For Exercises 13-18, use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. (See Example 2) InxeFor Exercises 13-18, use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. (See Example 2) logm2+n100For Exercises 13-18, use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. (See Example 2) log1000c2+119PEFor Exercises 19-24, apply the power property of logarithms. (See Example 3) log8t3221PEFor Exercises 19-24, apply the power property of logarithms. (See Example 3) log8x3423PEFor Exercises 19-24, apply the power property of logarithms. (See Example 3) ln0.5rtFor Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) log47yzFor Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) log25abFor Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) log717mn228PEFor Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) log2x10yz30PEFor Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) log6p5qt3For Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) log8a4b9cFor Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) log10a2+b2For Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) logd2+110,000For Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) lnxy3wz236PEFor Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) lna2+4e34For Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) lne2c2+55For Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) log2xx2+3843xFor Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) log5y4x+1727x3For Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) log5x53For Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) log2y24For Exercises 25-44, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. (See Example 4) log24a23bcb+4244PEFor Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) lny+ln446PEFor Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) log153+log155For Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) log128+log1218For Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) log798log72For Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) log6144log64For Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) log150log3log5For Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) log3693log333log37For Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) 2log2x+log2tFor Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) 5log4y+log4wFor Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) 4log8m3log8n2log8pFor Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) 8log3x2log3z7log3yFor Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) 3[lnxln(x+3)ln(x3)]For Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) 2[log(p4)log(p1)log(p+4)]For Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) 12lnx+112lnx1For Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) 13lnx2+113lnx+1For Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) 6logx13logy23logzFor Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) 15logc14logd34logkFor Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) 13log4p+log4q216log4q4For Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) 14log2w+log2w2100log2w+10For Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) 126lnx+2+lnxlnx266PEFor Exercises 45-68, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. (See Examples 5-6) log(8y27y)+logy168PE69PE70PE71PEFor Exercises 69-78, use logb20.356,logb30.565,andlogb50.827 to approximate the value of the given logarithms. (See Example 7) logb12573PEFor Exercises 69-78, use logb20.356,logb30.565,andlogb50.827 to approximate the value of the given logarithms. (See Example 7) logb12For Exercises 69-78, use logb20.356,logb30.565,andlogb50.827 to approximate the value of the given logarithms. (See Example 7) logb15276PEFor Exercises 69-78, use logb20.356,logb30.565,andlogb50.827 to approximate the value of the given logarithms. (See Example 7) logb100For Exercises 69-78, use logb20.356,logb30.565,andlogb50.827 to approximate the value of the given logarithms. (See Example 7) logb225For Exercises 79-84, (See Example 8) a. Estimate the value of the logarithm between two consecutive integers. For example, log27 is between 2 and 3 because 22723. b. Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places. c. Check the result by using the related exponential form. log215For Exercises 79-84, (See Example 8) a. Estimate the value of the logarithm between two consecutive integers. For example, log27 is between 2 and 3 because 22723. b. Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places. c. Check the result by using the related exponential form. log315For Exercises 79-84, (See Example 8) a. Estimate the value of the logarithm between two consecutive integers. For example, log27 is between 2 and 3 because 22723. b. Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places. c. Check the result by using the related exponential form. log53For Exercises 79-84, (See Example 8) a. Estimate the value of the logarithm between two consecutive integers. For example, log27 is between 2 and 3 because 22723. b. Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places. c. Check the result by using the related exponential form. log85For Exercises 79-84, (See Example 8) a. Estimate the value of the logarithm between two consecutive integers. For example, log27 is between 2 and 3 because 22723. b. Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places. c. Check the result by using the related exponential form. log20.3For Exercises 79-84, (See Example 8) a. Estimate the value of the logarithm between two consecutive integers. For example, log27 is between 2 and 3 because 22723. b. Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places. c. Check the result by using the related exponential form. log20.2For Exercises 85-88, use the change-of-base formula and a calculator to approximate the given logarithms. Round to 4 decimal places. Then check the answer by using the related exponential form. (See Example 8) log2(4.68107)For Exercises 85-88, use the change-of-base formula and a calculator to approximate the given logarithms. Round to 4 decimal places. Then check the answer by using the related exponential form. (See Example 8) log22.541010For Exercises 85-88, use the change-of-base formula and a calculator to approximate the given logarithms. Round to 4 decimal places. Then check the answer by using the related exponential form. (See Example 8) log45.68106For Exercises 85-88, use the change-of-base formula and a calculator to approximate the given logarithms. Round to 4 decimal places. Then check the answer by using the related exponential form. (See Example 8) log49.84105For Exercises 89-98, determine if the statement is true or false. For each false statement, provide a counterexample. For example, logx+ylogx+logy because log 2+8log2+log8 (the left side is 1 and the right side is approximately 1.204). loge=1ln10For Exercises 89-98, determine if the statement is true or false. For each false statement, provide a counterexample. For example, logx+ylogx+logy because log 2+8log2+log8 (the left side is 1 and the right side is approximately 1.204). ln10=1logeFor Exercises 89-98, determine if the statement is true or false. For each false statement, provide a counterexample. For example, logx+ylogx+logy because log 2+8log2+log8 (the left side is 1 and the right side is approximately 1.204). log51x=1log5xFor Exercises 89-98, determine if the statement is true or false. For each false statement, provide a counterexample. For example, logx+ylogx+logy because log 2+8log2+log8 (the left side is 1 and the right side is approximately 1.204). log61t=1log6tFor Exercises 89-98, determine if the statement is true or false. For each false statement, provide a counterexample. For example, logx+ylogx+logy because log 2+8log2+log8 (the left side is 1 and the right side is approximately 1.204). log41p=log4pFor Exercises 89-98, determine if the statement is true or false. For each false statement, provide a counterexample. For example, logx+ylogx+logy because log 2+8log2+log8 (the left side is 1 and the right side is approximately 1.204). log81w=log8wFor Exercises 89-98, determine if the statement is true or false. For each false statement, provide a counterexample. For example, logx+ylogx+logy because log 2+8log2+log8 (the left side is 1 and the right side is approximately 1.204). logxy=logxlogyFor Exercises 89-98, determine if the statement is true or false. For each false statement, provide a counterexample. For example, logx+ylogx+logy because log 2+8log2+log8 (the left side is 1 and the right side is approximately 1.204). logxy=logxlogyFor Exercises 89-98, determine if the statement is true or false. For each false statement, provide a counterexample. For example, logx+ylogx+logy because log 2+8log2+log8 (the left side is 1 and the right side is approximately 1.204). log27y+log21=log27yFor Exercises 89-98, determine if the statement is true or false. For each false statement, provide a counterexample. For example, logx+ylogx+logy because log 2+8log2+log8 (the left side is 1 and the right side is approximately 1.204). log43d+log41=log43dExplain why the product property of logarithms does not apply to the following statement. log55+log525=log5525=log5125=3Explain how to use the change-of-base formula and explain why it is important.a. Write the difference quotient for fx=lnx. b. Show that the difference quotient from part (a) can be written as lnx+hx1/h.Show that lnxx21=lnx+x21Show that logb+b24ac2a+logbb24ac2a=logclogaShow that lnc+c2x2cc2x2=2lnc+c2x22lnxUse the change-of-base formula to write log25log59 as a single logarithm.Use the change-of-base formula to write log311log114 as a single logarithm.Prove the quotient property of logarithms: logbxy=logbxlogby.Prove the power property of logarithms: logbxp=plogbx.For Exercises 109-112, graph the function. fx=log5x+4For Exercises 109-112, graph the function. gx=log7x3For Exercises 109-112, graph the function. kx=3+log1/2xFor Exercises 109-112, graph the function. hx=4+log1/3xa. Graph Y1=logxandY2=12logx2. How are the graphs related? b. Show algebraically that 12logx2=logx.Graph Y1=ln0.1x,Y2=ln0.5x,Y3=lnx,andY4=ln2x. How are the graphs related? Support your answer algebraically.Solve. a.42x3=64b.272w+5=1325wSolve. 5x=83Solve. a.400+104x1=63,000b.100=700e0.2kSolve. 35x6=24x+1Solve. e2x5ex14=0Solve. log27x4=log22x+1Solve. lnx+lnx8=lnx20Solve. 8log4w+6=24Solve. logt18=1.4Solve. 2log7x=log7x48Determine how long it will take $8000 compounded monthly at 6 to double. Round to 1 decimal place.a. Find the intensity of sound form a leaf blower it the decibel level is 115 dB. b. Is the intensity of sound from a leaf blower above the threshold for pain?An equation such as 4x=9 is called an equation because the equation contains a variable in the exponent.2PEThe equivalence property of logarithmic expressions states that if logbx=logby,then=.An equation containing a variable within a logarithmic expression is called a equation.For Exercises 5-16, solve the equation. (See Example 1) 3x=81For Exercises 5-16, solve the equation. (See Example 1) 2x=32For Exercises 5-16, solve the equation. (See Example 1) 53=5tFor Exercises 5-16, solve the equation. (See Example 1) 3=3wFor Exercises 5-16, solve the equation. (See Example 1) 23y+1=16For Exercises 5-16, solve the equation. (See Example 1) 52z+2=625For Exercises 5-16, solve the equation. (See Example 1) 113c+1=111c5For Exercises 5-16, solve the equation. (See Example 1) 72x3=149x+1For Exercises 5-16, solve the equation. (See Example 1) 82x5=32x6For Exercises 5-16, solve the equation. (See Example 1) 27x4=92x+1For Exercises 5-16, solve the equation. (See Example 1) 1003t5=10003tFor Exercises 5-16, solve the equation. (See Example 1) 100,0002w+1=10,0004wFor Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 6t=87For Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 2z=70For Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 1024=19x+4For Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 801=23y+6For Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 103+4x8100=120,000For Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 105+8x+4200=84,000For Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 21,000=63,000e0.2tFor Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 80=320e0.5tFor Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 4e2n5+3=11For Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 5e4m37=13For Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 36x+5=52xFor Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 74x1=35xFor Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 216x=73x+4For Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) 1118x=92x+3For Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) e2x9ex22=0For Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) e2x6ex16=0For Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) e2x=9exFor Exercises 17-34, solve the equation. Write the solution set the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. (See Example 2-5) e2x=7exFor Exercises 35-36, determine if the given value of x is a solution to the logarithmic equation. log2x31=5log2xa.x=16b.x=32c.x=1For Exercises 35-36, determine if the given value of x is a solution to the logarithmic equation. log4x=3log4x63a.x=64b.x=1c.x=32For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) log43w+11=log43wFor Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) log712t=log7t+6For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) logx2+7x=log18For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) logp2+6p=log7For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) 6log54p32=16For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) 5log67w+1+3=13For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) 2log83y5+20=24For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) 5log375z+2=17For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) logp+17=4.1For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) logq6=3.5For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) 2ln43t+1=7For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) 4ln65t+2=22For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) log2w3=log2w+2For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) log3y+log3y+6=3For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) log67x2=1+log6x+5For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) log45x13=1+log4x2For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) log5z=3log5z20For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) log2x=4log2x6For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) lnx+lnx4=ln3x10For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) lnx+lnx3=ln5x7For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) logx+logx7=logx15For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) logx+logx10=logx18For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) log86m+log8m1=1For Exercises 37-60, solve the equation. Write the solution set with the set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. (See Examples 6-10) log3n5+log3n+3=2For Exercises 61-70, use the model A=PertorA=P1+rnnt, where A is the future value of P dollars invested at interest rate r compounded continuously or n times per year for t years. (See Example 11) If $10,000 is invested in an account earning 5.5 Interest compounded continuously. determine how long it will take the money to triple. Round to the nearest year.For Exercises 61-70, use the model A=PertorA=P1+rnnt, where A is the future value of P dollars invested at interest rate r compounded continuously or n times per year for t years. (See Example 11) If a couple has $80,000 in a retirement account, how long will it take the money to grow to $1,000,000 if it grows by 6 compounded continuously? Round to the nearest year.For Exercises 61-70, use the model A=PertorA=P1+rnnt, where A is the future value of P dollars invested at interest rate r compounded continuously or n times per year for t years. (See Example 11) A $2500 bond grows to $3729.56 in 10 yr under continuous compounding. Find the interest rate. Round to the nearest whole percent.For Exercises 61-70, use the model A=PertorA=P1+rnnt, where A is the future value of P dollars invested at interest rate r compounded continuously or n times per year for t years. (See Example 11) $5000 grows to $5438.10 in 2 yr under continuous compounding. Find the interest rate. Round to the nearest tenth of a percent.For Exercises 61-70, use the model A=PertorA=P1+rnnt, where A is the future value of P dollars invested at interest rate r compounded continuously or n times per year for t years. (See Example 11) An $8000 investment grows to $9289.50 at 3 interest compounded quarterly. For how long was the money invested? Round to the nearest year.For Exercises 61-70, use the model A=PertorA=P1+rnnt, where A is the future value of P dollars invested at interest rate r compounded continuously or n times per year for t years. (See Example 11) $20,000 is invested at 3.5 interest compounded monthly. How long will it take for the investment to double? Round to the nearest tenth of a year.For Exercises 61-70, use the model A=PertorA=P1+rnnt, where A is the future value of P dollars invested at interest rate r compounded continuously or n times per year for t years. (See Example 11) A $25,000 inheritance is invested for 15 yr compounded quarterly and grows to $52,680. Find the interest rate. Round to the nearest percent.For Exercises 61-70, use the model A=PertorA=P1+rnnt, where A is the future value of P dollars invested at interest rate r compounded continuously or n times per year for t years. (See Example 11) A $10,000 investment grows to $11,273 in 4 yr compounded monthly. Find the interest rate. Round to the nearest percent.For Exercises 61-70, use the model A=PertorA=P1+rnnt, where A is the future value of P dollars invested at interest rate r compounded continuously or n times per year for t years. (See Example 11) If $4000 is put aside in a money market account with interest compounded continuously at 2.2, find the time required for the account to earn $1000 . Round to the nearest month.For Exercises 61-70, use the model A=PertorA=P1+rnnt, where A is the future value of P dollars invested at interest rate r compounded continuously or n times per year for t years. (See Example 11) Victor puts aside $10,000 in an account with interest compounded continuously at 2.7. How long will it take for him to earn $2000 ? Round to the nearest month.Physicians often treat thyroid cancer with a radioactive form of iodine called iodiro-131 131I . The radiological half-life of 131I is approximately 18 days, but the biological half-life for most individual is 4.2 days. The biological half-Ida is shorter because in addition to 131I being lost to decay, the iodine is also excreted from the body in urine, sweat, and saliva. For a patient treated with 100 mCi (millicuries) of 131I , the radioactivity level R (in mCi) after t days is given by R=1002t/4.2. a. State law mandates that the patient stay in an isolated hospital room for 2 days after treatment with 131I . Determine the radioactivity level at the end of 2 days. Round to the nearest whole unit. b. After the patient is released from the hospital, the patient is directed to avoid direct human contact until the radioactivity level drops below 30 mCi. For how many days after leaving the hospital will the patient need to stay in isolation? Round to the nearest tenth of a day.Caffeine occurs naturally in a variety of food products such as coffee, tea, and chocolate. The kidneys filter the blood and remove caffeine and other drugs through urine. The biological half-life of caffeine is approximately 6 hr. If one cup of coffee has 80 mg at caffeine, then the amount of caffeine C (in mg) remaining after hours is given by C=802t/6. a. How long ma it take for the amount of caffeine to drop below 60 mg? Round to 1 decimal place. b. Laura has trouble sleeping if she has more than 30 mg of caffeine in her bloodstream. How many hours after drinking a cup of coffee would Laura have to wait so that the coffee would not disrupt her sloop? Round to 1 decimal place.Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light, P (in decimal form). at a depth of x meters is given by P=ekx, where k Is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean. Lake Tahoe, and Lake Erie for data taken under similar conditions. Use these models for Exercises 73-76. Determine the depth at which the light intensity is half the value from the surface for each body of water given. Round to the nearest tenth of a meter.Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light, P (in decimal form). at a depth of x meters is given by P=ekx, where k Is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean. Lake Tahoe, and Lake Erie for data taken under similar conditions. Use these models for Exercises 73-76. Determine the depth at which the light intensity is 20 of the value from the surface for each body of water given. Round to the nearest tenth of a meter.Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light, P (in decimal form). at a depth of x meters is given by P=ekx, where k Is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean. Lake Tahoe, and Lake Erie for data taken under similar conditions. Use these models for Exercises 73-76. The euphoric depth is the depth at which light intensity falls to 1 of the value at the surface. This depth is of interest to scientists because no appreciable photosynthesis takes place. Find the euphotic depth for the open ocean. Round to the nearest tenth of a meter.Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light, P (in decimal form). at a depth of x meters is given by P=ekx, where k Is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean. Lake Tahoe, and Lake Erie for data taken under similar conditions. Use these models for Exercises 73-76. Refer to Exercise 75, and find the euphotic depth for Lake Tahoe and for Lake Erie. Round to the nearest tenth of a meter.Forge welding is a process in which two pieces of steel are joined together by heating the pieces of steel and hammering them together. A welder takes a piece of steel from a forge at 1600oF and places it on an anvil where the outdoor temperature is 50oF . The temperature of the steel TinoF can be modeled by T=50+1550e0.05t, where t is the time in minutes after the steel is removed from the forge. How long will it take for the steel to reach a temperature of 100oF so that it can be handled without heat protection? Round to the nearest minute.A pie comes out of the oven at 325oF and is placed to cool in a 70oF kitchen. The temperature of the pie TinoF after t minutes is given by T=70+255e0.017t. The pie is cool enough to cut when the temperature reaches 110F . How long will this take? Round to the nearest minute.79PEFor Exercises 79-80, the formula L=10logII0 gives the loudness of sound L (in dB) based on the intensity of sound IinW/m2 . The value I0=1012W/m2 is the minimal threshold for hearing for midfrequency sounds. Hearing impairment measured according to the minimal sound level (in dB) detected by an individual for sounds at various frequencies. For one frequency, the table depicts the level of hearing impairment. Determine the range that represents the intensity of sound that can be heard by an individual with severe hearing impairment.81PE82PEA new teaching method to teach vocabulary to sixth-graders involves having students work in group on an assignment to learn new words. After lesson was completed, the students were tested at 1-month intervals. The average score for the class St can be modeled by St=9418lnt+1 where t is the time in months after completing the assignment. If the average score is 65, how many months had passed since the students completed the assignment? Round to the nearest month.84PERadiated seismic energy from an earthquake is estimated by logE=4.4+1.5M, where E is the energy in Joules JandM is surface wave magnitude. a. How many times more energy does an 8.2-magnitude earthquake have than a 5.5-magnitude earthquake? Round to the nearest thousand. b. How many times more energy does a 7-magntude earthquake have than a 6-inagoitude earthquake? Round to the nearest whole number.On August 31, 1854, an epidemic of cholera was discovered in London, England, resulting from a contaminate community water pump. By the end of September more than 600 citizens who drank water from the pump had died. The cumulative number of deaths Dt at a time t days after August 31 is given by Dt=91+160lnt+1. a. Determine the Cumulative number of deaths by September 15. Round to the nearest whole unit. b. Approximately how many days after August 31 did the cumulative number of deaths reach 600?For Exercises 87-94, find an equation for the inverse function. fx=2x7For Exercises 87-94, find an equation for the inverse function. fx=5x+6For Exercises 87-94, find an equation for the inverse function. fx=lnx+5For Exercises 87-94, find an equation for the inverse function. fx=lnx7For Exercises 87-94, find an equation for the inverse function. fx=10x3+1For Exercises 87-94, find an equation for the inverse function. fx=10x+24For Exercises 87-94, find an equation for the inverse function. fx=logx+79For Exercises 87-94, find an equation for the inverse function. fx=logx11+8For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. 5x3=122For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. 11x+9=130For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. logx2log3=2For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. logy3log5=3For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. 6x22=36For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. 8y27=64For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. log9x+4=log96For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. log83x=log85For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. x2ex=9ex104PEFor Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. log3log3x=0For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. log5log5x=1For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. 3lnx12=0For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. 7lnx14=0For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. log3xlog32x+6=12log34For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. log5xlog5x+1=13log58For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. 2exex3=3ex4For Exercises 95-112, solve the equation. Write the solution set with exact solutions. Also give approximate solutions to 4 decimal places if necessary. 3exex6=4ex7Explain the process to solve the equation 4x=11.114PE115PEFor Exercises 115-126, solve the equation. ex9ex2=4For Exercises 115-126, solve the equation. lnx2lnx5=4118PEFor Exercises 115-126, solve the equation. logx2=logx2For Exercises 115-126, solve the equation. logx2=logx3For Exercises 115-126, solve the equation. logw+4logw12=0For Exercises 115-126, solve the equation. lnx+3lnx10=0For Exercises 115-126, solve the equation. e2x8ex+6=0For Exercises 115-126, solve the equation. e2x6ex+4=0For Exercises 115-126, solve the equation. log56c+5+log5c=1For Exercises 115-126, solve the equation. log3x8+log3x=1For Exercises 127-130, an equation is given in the form Y1x=Y2x. Graph Y1andY2 on a graphing utility on the window 10,10,1by10,10,1 . Then approximate the point(s) of intersection to approximate the solution(s) to the equation. Round to 4 decimal places. 4xex+6=0For Exercises 127-130, an equation is given in the form Y1x=Y2x. Graph Y1andY2 on a graphing utility on the window 10,10,1by10,10,1 . Then approximate the point(s) of intersection to approximate the solution(s) to the equation. Round to 4 decimal places. x3e2x+4=0For Exercises 127-130, an equation is given in the form Y1x=Y2x. Graph Y1andY2 on a graphing utility on the window 10,10,1by10,10,1 . Then approximate the point(s) of intersection to approximate the solution(s) to the equation. Round to 4 decimal places. x2+5logx=6For Exercises 127-130, an equation is given in the form Y1x=Y2x. Graph Y1andY2 on a graphing utility on the window 10,10,1by10,10,1 . Then approximate the point(s) of intersection to approximate the solution(s) to the equation. Round to 4 decimal places. x20.05lnx=4a. Given T=78+272ekt,solvefork. b. Given S=9020lnt+1,solvefort.