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...
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Question
109,115 please
![Fd the value of log: 3- log, 4. log. (n+ 1) log2. 10e. Find the value of log; 2- log 4-log; 8 log 2.
t Find the value of log; 3- log, 4- log, 5- logs 6. log, 7- log, 8. 98. Find the value of log; 4-log,6-log, 8.
Ierence Quotient If f(x) - log, x, show that A)-f)- log.1+).
Gompressing or stretching, and reflecting. State the domain
- express y as a function of x. The constant C is a positive number
SECTION SS Properties of Logarithms 317
in+ In C
SA. Iny-In(x + C)
90. In y-2 in I- In(x+ 1) + In C
92. In y- -2x + In C
94. In (y + 4) -Sx + In C
96. 2 In y- Inx in(+ 1) + In C
tar+ In C
- 3)- -4r + lnC
a(2x + 1) - In (x + 4) + In C
In ain( + 1) + In C
ihat log. (x + V - 1) + log,(x - V - 1) - 0
that log. (Va+ Vx - 1) + log.(Vĩ - VI-1) -0
that In (1 + )- 2r + In (1 +).
f(x+ h) - f(x)
log
+]
) - log, K, show that -/(x) - log x.
106. If f(x) - log, x, show that f(AB) (A) + S(B).
) - log, K, show that ) - -f(x).
Sow that log.N)- log, M - log, N, where a, M, and N
.
108. If f(x) = log, x, show that f(x) = af(x).
110. Show that log,) - -log, N, where a and N are positive
positive real numbers and a 1.
real numbers and a+ 1.
log, a where a
and b are positive real numbers, a 1, and b 1.
IL Challenge Problem Show that log, b-
112. Challenge Problem Show that log vm- log, m",
where a and m are positive real numbers and a 1.
A Challenge Problem Show that log, b" = " log, b.
shere a, b, m, and n are positive real numbers, a 1,
and b1.
114. Challenge Problem Find n:
log; 3- log, 4- log, 5.... •log. (n + 1) = 10
Explaining Concepts: Discussion and Writing
5 Graph Y = log (x) and Y; - 2 log (x) using a graphing
utility. Are they equivalent? What might sonount for any
dierences in the two functions?
IK Write an example that illustrates why (log. rlog, x.
117. Write an example that illustrates why
24
log:(x + y) log, x + log: y
118. Does 3(-5)- -5? Why or why not?
Retain Your Knowledge
ma 119-128 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in
mind so that you are better prepared for the final exam.
2V3 - Sx - 4.
Ule a graphing utility to solve r- 3 - 4x + 8-0.
Round answers to twodecimal places
Nilhout solving, determine the character of the solution of
adratic equation 4x - 28r + 49 = 0 in the complex
123. Find the domain of f(x) -
124. Solve: 4|x + 1 -9 < 23
125. Find the vertex of f(x) = - +
4x + 5, and determine
umber system.
if the graph is concave up or concave down.
L Find the real zeros of
126. Find the center and radius of the circle
- 10x + y + 4y = 35
(x) = 5x + 44x + 116 + 95x- 4x - 4
-r from -1 to 3.
S - 3x
even, odd, or neither?
anding or stretching, and reflecting. State the domain A128. Is the function f(x) =
the range of f.
Vi](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fcc2212-54a6-4f1d-b6b8-1f7f4adab2ee%2F7d7591a1-d49e-4437-9df4-c9ea06ff42b6%2F5f1rumm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Fd the value of log: 3- log, 4. log. (n+ 1) log2. 10e. Find the value of log; 2- log 4-log; 8 log 2.
t Find the value of log; 3- log, 4- log, 5- logs 6. log, 7- log, 8. 98. Find the value of log; 4-log,6-log, 8.
Ierence Quotient If f(x) - log, x, show that A)-f)- log.1+).
Gompressing or stretching, and reflecting. State the domain
- express y as a function of x. The constant C is a positive number
SECTION SS Properties of Logarithms 317
in+ In C
SA. Iny-In(x + C)
90. In y-2 in I- In(x+ 1) + In C
92. In y- -2x + In C
94. In (y + 4) -Sx + In C
96. 2 In y- Inx in(+ 1) + In C
tar+ In C
- 3)- -4r + lnC
a(2x + 1) - In (x + 4) + In C
In ain( + 1) + In C
ihat log. (x + V - 1) + log,(x - V - 1) - 0
that log. (Va+ Vx - 1) + log.(Vĩ - VI-1) -0
that In (1 + )- 2r + In (1 +).
f(x+ h) - f(x)
log
+]
) - log, K, show that -/(x) - log x.
106. If f(x) - log, x, show that f(AB) (A) + S(B).
) - log, K, show that ) - -f(x).
Sow that log.N)- log, M - log, N, where a, M, and N
.
108. If f(x) = log, x, show that f(x) = af(x).
110. Show that log,) - -log, N, where a and N are positive
positive real numbers and a 1.
real numbers and a+ 1.
log, a where a
and b are positive real numbers, a 1, and b 1.
IL Challenge Problem Show that log, b-
112. Challenge Problem Show that log vm- log, m",
where a and m are positive real numbers and a 1.
A Challenge Problem Show that log, b" = " log, b.
shere a, b, m, and n are positive real numbers, a 1,
and b1.
114. Challenge Problem Find n:
log; 3- log, 4- log, 5.... •log. (n + 1) = 10
Explaining Concepts: Discussion and Writing
5 Graph Y = log (x) and Y; - 2 log (x) using a graphing
utility. Are they equivalent? What might sonount for any
dierences in the two functions?
IK Write an example that illustrates why (log. rlog, x.
117. Write an example that illustrates why
24
log:(x + y) log, x + log: y
118. Does 3(-5)- -5? Why or why not?
Retain Your Knowledge
ma 119-128 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in
mind so that you are better prepared for the final exam.
2V3 - Sx - 4.
Ule a graphing utility to solve r- 3 - 4x + 8-0.
Round answers to twodecimal places
Nilhout solving, determine the character of the solution of
adratic equation 4x - 28r + 49 = 0 in the complex
123. Find the domain of f(x) -
124. Solve: 4|x + 1 -9 < 23
125. Find the vertex of f(x) = - +
4x + 5, and determine
umber system.
if the graph is concave up or concave down.
L Find the real zeros of
126. Find the center and radius of the circle
- 10x + y + 4y = 35
(x) = 5x + 44x + 116 + 95x- 4x - 4
-r from -1 to 3.
S - 3x
even, odd, or neither?
anding or stretching, and reflecting. State the domain A128. Is the function f(x) =
the range of f.
Vi
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