25,31 In Problems l1-14, each function is one-to-one. Find the inverse of each function and check your answer. Find the domain and range of f and f1(a) What is the limiting magnitude of a 3.5-inch telescope?356 CHAPTER 5 Exponential and Logarithmic Functions14. f(x) = x + 12r + 313. f(x) = Vx – 211. f(x) =12. f(x) =5x - 215. Given f(x) = 3" and g(x)= loga x, evaluate each of the following.(d)(a) f(4)(b) g(9)(c) f(-2)16. Change 52 = z to an equivalent statement involving a logarithm.17. Change logs u = 13 to an equivalent statement involving an exponent.In Problems 18 and 19, find the domain of each logarithmic function.19. H(x) = log2 (x² – 3x + 2)18. f(x) = log (3x – 2)In Problems 20-22, find the exact value of each expression, Do not use a calculator.22. 2lo820.420. log221. In eVIn Problems 23-26, write each expression as the sum and/or difference of logarithms. Express powers as factors.24. log2 (a? Vb)“ a > 0, b > 023. log,()uvu > 0, v > 0, w >02x + 326. In 2- 3x + 2)x > 225. log (x? Vx + 1) x > 0In Problems 27-29, write each expression as a single logarithm.log, VaIn) + In) - In(x² – 1)27. 3 log4 x? +국n (12 + 1)-4In -In(x-4) + Inx]29.30. Use the Change-of-Base Formula and a calculator to evaluate log, 19. Round your answer to three decimal places.31. Graph y = log3 x using a graphing utility and the Change-of-Base Formula.In Problems 32–35, for each function f:(a) Find the domain of f.(d) Find f-1, the inverse function of f.(c) From the graph, determine the range and any asymptotes of f.() Graph f1.(b) Graph f.(e) Find the domain and the range of f.32. f(x) = 2"-333. f(x) = 1 + 3-*34. f(x) = 3e*-235. f(x) = ;x + 3)In Problems 36-46, solve each equation. Express irrational solutions in exact form.36. 86+3x = 437. 3*+* = V338. log, 64 = -339, 5* = 3*+240. 252x = 5-1241. log3 Vx – 2 = 242. 8 = 4. 25x43. 2 .5 = 10"44. log, (x + 3) + log, (x + 4) = 145. el-x = 546. 9* + 4.3* - 3 = 047. Suppose that f(x) = log2(x – 2) + 1.(a) Graph f.(b) What is f(6)? What point is on the graph of f ?(c) Solve f(x) = 4. What point is on the graph of f?(d) Based on the graph drawn in part (a), solve f(x) > 0.(e) Find f (x). Graph f on the same Cartesian plane49. Limiting Magnitude of a Telescope A telescope is limilein its usefulness by the brightness of the star that it is ailat and by the diameter of its lens One measure of a stai sbrightness is its magnitude: the dimmer the star, the lalgeits magnitude. A formula for the limiting magnitude Ltelescope-that is, the magnitude of the dimmest star tiecan be used to view-is given byas f.48. Amplifying Sound An amplifier's power output P (in watts)is related to its decibel voltage gain d by the formulaL = 9 + 5.1 log dwhere d is the diameter (in inches) of the lens.P = 25e0.ld(a) Find the power output for a decibel voltage gainof 4 decibels.(b) For a power output of 50 watts, what is the decibelvoltage gain?

Name: 25,31 In Problems l1-14, each function is one-to-one. Find the inverse
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 25,31 In Problems l1-14, each function is one-to-one. Find the inverse of each function and check your answer. Find the domain and range of f and f1(a) What is the limiting magnitude of a 3.5-inch telescope?356 CHAPTER 5 Exponential and Logarithmic F

As per the company guidelines we can solve first question. I hope that the given solution will help…

Math

Calculus

In Problems 23-26, write each expression as the sum and/or difference of logarithms. Express powers as factors. uv 23. log3 u > 0, v > 0, w >0 24. log2 (a? Vb)* a> 0, b> 0 25. log (x Vx + 1) x > 0 2r + 3 x > 2 26. In 2-3r +2)

In Problems 23-26, write each expression as the sum and/or difference of logarithms. Express powers as factors. uv 23. log3 u > 0, v > 0, w >0 24. log2 (a? Vb)* a> 0, b> 0 25. log (x Vx + 1) x > 0 2r + 3 x > 2 26. In 2-3r +2)

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section: Chapter Questions

Problem 30P: In this problem you are asked to find a function that models in real life situation and then use the...

See similar textbooks

Related questions

Q: 3dt =. O 24 12 16 20 O 3

Q: 3. 3 de dy 40

Q: A cell phone company claims that the average time a person spends on their phone is 12.8 hours a…

A: Given that, Population mean=μ=12.8 Hours Sample mean=X Bar=12.2 Hours Sample standard deviation= 2.3…

Q: 75 17

A: Given triangle is right angle triangle :

Q: 16,17,18

Q: 22. 792 +33%3D %3D 23. 811 4 35/792 26. 33)9,537 27. 19)4.

Q: The accompanying table lists the ages of acting award winners matched by the years in which the…

A: In this case consider Best actress as the independent variable and Best Actor is the dependent…

Q: 72 44

A: Given: In the right-angle triangle, assume that the missing angle is y So we know that the addition…

Q: 3. 2 2 .b O 3 4 3.

Q: 4. 12, 15, and 17

A: Since you have asked multiple questions in single request, So we will be answering only first…

Q: 3. Find the rank of 0 2 4 1 21 6 6 6 2 - -m0 + O

Q: 12 16 5n

A: Area of triangle= (1/2) × Base × Height

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

25,31

In Problems l1-14, each function is one-to-one. Find the inverse of each function and check your answer. Find the domain and range of f and f1
(a) What is the limiting magnitude of a 3.5-inch telescope?
356 CHAPTER 5 Exponential and Logarithmic Functions
14. f(x) = x + 1
2r + 3
13. f(x) = Vx – 2
11. f(x) =
12. f(x) =
5x - 2
15. Given f(x) = 3" and g(x)= loga x, evaluate each of the following.
(d)
(a) f(4)
(b) g(9)
(c) f(-2)
16. Change 52 = z to an equivalent statement involving a logarithm.
17. Change logs u = 13 to an equivalent statement involving an exponent.
In Problems 18 and 19, find the domain of each logarithmic function.
19. H(x) = log2 (x² – 3x + 2)
18. f(x) = log (3x – 2)
In Problems 20-22, find the exact value of each expression, Do not use a calculator.
22. 2lo820.4
20. log2
21. In eV
In Problems 23-26, write each expression as the sum and/or difference of logarithms. Express powers as factors.
24. log2 (a? Vb)“ a > 0, b > 0
23. log,()
uv
u > 0, v > 0, w >0
2x + 3
26. In 2- 3x + 2)
x > 2
25. log (x? Vx + 1) x > 0
In Problems 27-29, write each expression as a single logarithm.
log, Va
In) + In) - In(x² – 1)
27. 3 log4 x? +
국n (12 + 1)-4In -In(x-4) + Inx]
29.
30. Use the Change-of-Base Formula and a calculator to evaluate log, 19. Round your answer to three decimal places.
31. Graph y = log3 x using a graphing utility and the Change-of-Base Formula.
In Problems 32–35, for each function f:
(a) Find the domain of f.
(d) Find f-1, the inverse function of f.
(c) From the graph, determine the range and any asymptotes of f.
() Graph f1.
(b) Graph f.
(e) Find the domain and the range of f.
32. f(x) = 2"-3
33. f(x) = 1 + 3-*
34. f(x) = 3e*-2
35. f(x) = ;
x + 3)
In Problems 36-46, solve each equation. Express irrational solutions in exact form.
36. 86+3x = 4
37. 3*+* = V3
38. log, 64 = -3
39, 5* = 3*+2
40. 252x = 5-12
41. log3 Vx – 2 = 2
42. 8 = 4. 25x
43. 2 .5 = 10"
44. log, (x + 3) + log, (x + 4) = 1
45. el-x = 5
46. 9* + 4.3* - 3 = 0
47. Suppose that f(x) = log2(x – 2) + 1.
(a) Graph f.
(b) What is f(6)? What point is on the graph of f ?
(c) Solve f(x) = 4. What point is on the graph of f?
(d) Based on the graph drawn in part (a), solve f(x) > 0.
(e) Find f (x). Graph f on the same Cartesian plane
49. Limiting Magnitude of a Telescope A telescope is limile
in its usefulness by the brightness of the star that it is ail
at and by the diameter of its lens One measure of a stai s
brightness is its magnitude: the dimmer the star, the lalge
its magnitude. A formula for the limiting magnitude L
telescope-that is, the magnitude of the dimmest star tie
can be used to view-is given by
as f.
48. Amplifying Sound An amplifier's power output P (in watts)
is related to its decibel voltage gain d by the formula
L = 9 + 5.1 log d
where d is the diameter (in inches) of the lens.
P = 25e0.ld
(a) Find the power output for a decibel voltage gain
of 4 decibels.
(b) For a power output of 50 watts, what is the decibel
voltage gain?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Discrete Probability Distributions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.
The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.
When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal shift from a vertical shift?
Are one-to-one functions either always increasing or always decreasing? Why or why not?
Determine whether Table 1 could represent a function that is linear, exponential, or neither. If it appears to beexponential find a function that passes through the points.
Find the inverse function f1 for the exponential function f(x)=2ex+15.
The graph of fx=1/x is a .
What strategy would you use to graph fx=log5x?
In this problem you are asked to find a function that models in real life situation and then use the model to answer questions about the guidelines on page 273 to help you. Minimizing Time A man stands at a point A on the bank of a straight river, 2 mi wide. To reach point B, 7 mi downstream on the opposite bank, he first rows his boat to point Pon the opposite bank and then walks the remaining distances x to B, as shown in the figure. He can row at a speed or 2 mi/h and walk as a speed of mi/h (a) Find a function that models the time needed for the trip. (b) Where should he land so that he reaches B as soon as possible?
Use a calculator to help solve each problem. Life expetctancy The life expectancy l of white females can be estimated by using the function lx=78.51.001x, where x is the current age. Find the life expectancy of a white female who is currently 50 years old. Give the answer to the nearest tenth.
The inverse of every logarithmic function is anexponential function and vice-versa. What doesthis tell us about the relationship between thecoordinates of the points on the graphs ofeach?
How do you find the inverse of a function algebraically?