Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
37,43,49
![(b) What diameter is required to view a star of magnitude
(a) What is the limiting magnitude of a 3.5-inch telesop
356 CHAPTER 5 Exponential and Logarithmic Functions
14. f(x) = x +
2r + 3
13. f(x) = Vr - 2
50. Salvage
to dep
11. f(x) =
Sx- 2
12. (x) =
G)
the for
(d)
(a) f(4)
(b) g(9)
(c) f(-2)
16. Change 5 = z to an equjvalent statement involving a logaritnim.
where
In Problems 18 and 19, find the domain of each logarithmic junchon.
18. f(x) = log (3x – 2)
value
(a) F
19. H(x) = log2(x² – 3x + 2)
20. log:
22. 2lo820.4
(b)
21. In eV2
ncolems 23-20, write each expression as the sum and/or difference of logarithms. Express powers as factors
23. log3
24. log2 (a? Vb)* a> 0, b > 0
51. Fun
u > 0, v > 0, w > 0
pur
be
25. log (x Vx + 1) x > 0
2x + 3
26. In
2- 3x + 2)
x > 2
inte
bo
of
In Problems 27-29, write each expression as a single logarithm.
un
27. 3 log4 x² +
2 log, Va
52. Fu
pu
28.
+
희in( + 1)-4m-글[In(x - 4) + Inx]
CC
29.
se
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.
53. E
In Problems 32–35, for each function f:
(a) Find the domain of f.
(d) Find f1, the inverse function of f.
(c) From the graph, determine the range and any asymptotes of f
(b) Graph f.
(e) Find the domain and the range of f.
(f) Graph f~1.
54.
32. f(x) = 2*-3
33. f(x) = 1 + 3-*
34. f(x) = 3e*-2
In Problems 36-46, solve each equation. Express irrational solutions in exact form.
35. f(x) =
n(x+3)
36. 86+3x = 4
37. 3r+x = V3
41. log, Vx - 2 = 2
55.
40. 252r = 5r-12
38. log, 64 = - 3
39. 5* = 3*+2
44. log, (x + 3) + log6 (x + 4) = 1
42. 8 = 4.25
45. el-x = 5
43. 2* .5 = 10"
46. 9* + 4.3 -- 3 = 0
47. Suppose that f(x) = log2(x – 2) + 1.
56
(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
as f.
49. Limiting Magritie of a Telescope A telescope is limit.
in its usefulness b the brightness of the star that it is aim
at and by the diameter of its lens. One measure of a str
brightness is its magnitude; the dimmer the star, the lag
its magnitude. A formula for the limiting magnitude Lal
telescope-that is, the magnitude of the dimmest star li
can be used to view-is given by
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 = 25e0.1d
(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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed398b18-d726-4d2c-b4f7-dcea12dc23a3%2Ff3b4eb7e-b08a-449b-96f6-6d8a857d8811%2F4vcauwm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) What diameter is required to view a star of magnitude
(a) What is the limiting magnitude of a 3.5-inch telesop
356 CHAPTER 5 Exponential and Logarithmic Functions
14. f(x) = x +
2r + 3
13. f(x) = Vr - 2
50. Salvage
to dep
11. f(x) =
Sx- 2
12. (x) =
G)
the for
(d)
(a) f(4)
(b) g(9)
(c) f(-2)
16. Change 5 = z to an equjvalent statement involving a logaritnim.
where
In Problems 18 and 19, find the domain of each logarithmic junchon.
18. f(x) = log (3x – 2)
value
(a) F
19. H(x) = log2(x² – 3x + 2)
20. log:
22. 2lo820.4
(b)
21. In eV2
ncolems 23-20, write each expression as the sum and/or difference of logarithms. Express powers as factors
23. log3
24. log2 (a? Vb)* a> 0, b > 0
51. Fun
u > 0, v > 0, w > 0
pur
be
25. log (x Vx + 1) x > 0
2x + 3
26. In
2- 3x + 2)
x > 2
inte
bo
of
In Problems 27-29, write each expression as a single logarithm.
un
27. 3 log4 x² +
2 log, Va
52. Fu
pu
28.
+
희in( + 1)-4m-글[In(x - 4) + Inx]
CC
29.
se
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.
53. E
In Problems 32–35, for each function f:
(a) Find the domain of f.
(d) Find f1, the inverse function of f.
(c) From the graph, determine the range and any asymptotes of f
(b) Graph f.
(e) Find the domain and the range of f.
(f) Graph f~1.
54.
32. f(x) = 2*-3
33. f(x) = 1 + 3-*
34. f(x) = 3e*-2
In Problems 36-46, solve each equation. Express irrational solutions in exact form.
35. f(x) =
n(x+3)
36. 86+3x = 4
37. 3r+x = V3
41. log, Vx - 2 = 2
55.
40. 252r = 5r-12
38. log, 64 = - 3
39. 5* = 3*+2
44. log, (x + 3) + log6 (x + 4) = 1
42. 8 = 4.25
45. el-x = 5
43. 2* .5 = 10"
46. 9* + 4.3 -- 3 = 0
47. Suppose that f(x) = log2(x – 2) + 1.
56
(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
as f.
49. Limiting Magritie of a Telescope A telescope is limit.
in its usefulness b the brightness of the star that it is aim
at and by the diameter of its lens. One measure of a str
brightness is its magnitude; the dimmer the star, the lag
its magnitude. A formula for the limiting magnitude Lal
telescope-that is, the magnitude of the dimmest star li
can be used to view-is given by
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 = 25e0.1d
(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?
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