Is the base 2 logarithm of 3, log₂ 3, a rational number or an irrational number? Justify your conclusion.

Q: For any real number b > 1, and any real numbers x True False log, (x - y) = > 0 and y> 0, it must be…

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Q: 5. Condense/compress the expression to one term in (i) and (ii), and expand the expression in terms…

A: Find your answer below

Q: Show the following statement and justify each of your steps for the solution with valid mathematical…

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Q: 1) log3 4 + log2 9 + In 20 1 2) log6 42 ' log7 42 1

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Q: 1. Use your logarithm rules to evaluate each of the following. Round to 2 decimal places where…

A: As per the guideline, I am supposed to solve only  first three sub-parts of the given problem.

Q: 2. Suppose that f(x) = ((.x² + x·5).5 +.r.5).5 when x ≥ 0. Find df(x)/dx. •5 (@ï¥2³ )² +x²)+…

A: The answer is given in step 2

Q: 5. Determine whether the following are rational numbers: (a) 2² +27¹; (b) log₂ 3; (c) 2+√2. (d) If…

A: We have to find if the given numbers are rational or not.

Q: What is the domain of the function g(z) = 3 log, (x – 1) + 4? Enter your answer in the box. All real…

A: Solution-

Q: Express log; M+4log, Nas a 3 single logarithm. M a) log; b) log, (M'³N*) M c) log; d) log; (MN) O a…

A: To Express in single logarithm

Q: Please help me solve the followng equation

A: The given equation…

Q: 1) (20 pts) If log, = X, express log, in terms of x 2) (40 pts) Simplify and find the value of 1 1 1…

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Q: Which value of X is not in the domain of the function G(x)=26/15x-29" I am a little confused by the…

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Q: 5. Solve log (5x² - 5x − 8) = log(5x - 2) (x - 1).

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Q: 7. If log, w = and log6x + log6 y = 1, then determine the value of log7 (4) + log6 (36x²y²) ?|

A: topic- logarithmic equations logaa=1log(ab)=log(a)+log(b)logab=log(a)=log(b)log(am)=mlog(a)

Q: Let b be a real number. By considering properties of exponential functions, show that the points…

A: We know, for any real number b > 1,         b0 = 1      => logb(b0) = logb(1)       =>…

Q: 7. Given the functions f(x) = log₂ (x-1) and g(x) = log₂ (9-x²), c) Determine (f-g)(x). b) State the…

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Q: 10. Algebraically determine how long, to the nearest tenth of a month, it takes the smartphone to be…

A: Use log properties to solve the question.  Log table or log calculated needs to be used.

Q: Provide an appropriate response. Find f'(x) for f(x) = log6(x + 1) %3D Select one: A. 9x8 (In 6)(x+…

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Q: Problem Set: B (1) Solve the following: (a) 4*-1 = 64 (b) 8- =4*+2 (c) 22 + 2 -12 = 0 (e) log.(x+…

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Q: A) fex) = (x + log (log (3²+x²)) ; f(x)= O(³√x) B) f(x)= lg (2²-x²); f(x) € (x) A. Only A is TRUE B.…

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Q: Solve for all possible values of x. Use exact values. a) log x – log 3 = log 13 + log 2 b) log.(x +…

A: Solving the problem by obtaining the values of x and n.

Q: have to find all the solutions for the equations and I keep finding 1 but it tells me I’m wrong

A: We Will find the solution. Try adding parentheses as mentioned since the solution is correct.

Q: Prove that th followijg is true forx, y > 0. Please show all steps log(1+ xy) log(1+x)log (1+y) a c…

A: The logarithm inequality is :Where,The aim is to prove this logarithm inequality.

Q: Q1: prove the following: a. Prove that For all real numbers x and y, if x +y 22, then either x ≥1 or…

A: a. We will prove  for all real numbers x and y, if       x + y ≥ 2 , then either x ≥ 1 or y ≥ 1 by…

Q: 1. Evaluate log381 + log,64 a. 5184 log 81 log 3 + 4 64 (6.) 7 c. 1 Af d. 145 = 71 2. Express logma…

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Q: You are given the integral 64x2 - 81 dr. I = 6x In order to compute this integral, we may attack…

A: To find out the integration.

Q: Prove by contradiction: "log4575 is irrational."

A: To prove that log4575 is irrational

Q: The equation log10 (2x-3) = 0 has solution: 0₁)=4 2) None of the choices here are correct 032=2 042…

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Q: 9. Solve each question below – show all steps for full marks and reject all extraneous roots! a.…

A: Use the property am=an implies m=n