Question 1

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$\ln \sqrt { x + 2 } = 4$

Accepted Answer

A)  $\left\{ e ^ { 4 } - 2 \right\}$ 
B)  $\left\{ e ^ { 8 } - 2 \right\}$ 
C)  $\left\{ e ^ { 8 } + 2 \right\}$ 
D)  $\left\{ \frac { \mathrm { e } ^ { 4 } } { 2 } + 2 \right\}$ 
A)  $\left\{ e ^ { 4 } - 2 \right\}$ 
B)  $\left\{ e ^ { 8 } - 2 \right\}$ 
C)  $\left\{ e ^ { 8 } + 2 \right\}$ 
D)  $\left\{ \frac { \mathrm { e } ^ { 4 } } { 2 } + 2 \right\}$

Question 2

Find the exact value of the logarithmic expression.
-$\log _ { 4 } 16$

Accepted Answer

A)  2 
B)  8 
C)  16 
D)  4 
A)  2 
B)  8 
C)  16 
D)  4

Question 3

Choose the one alternative that best completes the statement or answers the question.
-The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential
) How much did you initially invest in the account? $$\text { growth model } \mathrm { A } = 5,300 \mathrm { e } ^ { 0.045 \mathrm { t } }$$

Accepted Answer

A)  $2,650.00 
B)  $5,543.95 
C)  $238.50 
D)  $5,300.00 
A)  $2,650.00 
B)  $5,543.95 
C)  $238.50 
D)  $5,300.00

Question 4

Find functions f and g so that f ° g = H.
-$$H ( x ) = | 9 x + 3 |$$

Accepted Answer

A)  $f ( x ) = | - x | ; \quad g ( x ) = 9 x - 3$ 
B)  $f ( x ) = - | x |$
$g ( x ) = 9 x + 3$ 
C)  $f ( x ) = x ; g ( x ) = 9 x + 3$ 
D)  $f ( x ) = | x | ; \quad g ( x ) = 9 x + 3$ 
A)  $f ( x ) = | - x | ; \quad g ( x ) = 9 x - 3$ 
B)  $f ( x ) = - | x |$
$g ( x ) = 9 x + 3$ 
C)  $f ( x ) = x ; g ( x ) = 9 x + 3$ 
D)  $f ( x ) = | x | ; \quad g ( x ) = 9 x + 3$

Question 5

Find the domain of the function.
-$$f ( x ) = \log _ { 6 } \left( 36 - x ^ { 2 } \right)$$

Accepted Answer

A)  $- 36  6$ 
A)  $- 36  6$

Question 6

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$\log _ { 6 } \left( x ^ { 2 } - 5 x \right) = 1$

Accepted Answer

A)  $\{ - 6,1 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 6 , - 1 \}$ 
D)  $\{ 1 \}$ 
A)  $\{ - 6,1 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 6 , - 1 \}$ 
D)  $\{ 1 \}$

Question 7

The function f is one-to-one. Find its inverse.
-$$f ( x ) = 2 x$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = - 2 x$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { 2 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 2 } { x }$ 
D)  $f ^ { - 1 } ( x ) = 2 x$ 
A)  $f ^ { - 1 } ( x ) = - 2 x$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { 2 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 2 } { x }$ 
D)  $f ^ { - 1 } ( x ) = 2 x$

Question 8

Write the word or phrase that best completes each statement or answers the question.
-John Forgetsalot deposited $100 at a 3% annual interest rate in a savings account fifty years ago, and then he
promptly forgot he had done it. Recently, he was cleaning out his home office and discovered the forgotten
bank book. How much money is in the account?

Accepted Answer

The answer of Write the word or phrase that best...

Question 9

For the given functions f and g, find the requested composite function.
-$f ( x ) = \frac { x - 10 } { 2 } , g ( x ) = 2 x + 10 ; \quad$ Find $( g \circ f ) ( x )$

Accepted Answer

A)  $x$ 
B)  $2 x + 10$ 
C)  $x - 5$ 
D)  $x + 20$ 
A)  $x$ 
B)  $2 x + 10$ 
C)  $x - 5$ 
D)  $x + 20$

Question 10

Use a calculator to find the natural logarithm correct to four decimal places.
-$\ln 200$

Accepted Answer

A)  $73.8007$ 
B)  $0.1882$ 
C)  $5.2983$ 
D)  $2.3010$ 
A)  $73.8007$ 
B)  $0.1882$ 
C)  $5.2983$ 
D)  $2.3010$

Question 11

Write as the sum and/or difference of logarithms. Express powers as factors.
-$\log _ { 2 } \left( \frac { x + 5 } { x ^ { 7 } } \right)$

Accepted Answer

A)  $\log _ { 2 } ( x + 5 ) - 7 \log _ { 2 } x$ 
B)  $\log _ { 2 } ( x + 5 ) + 7 \log _ { 2 } x$ 
C)  $\log _ { 2 } ( x + 5 ) - \log _ { 2 } x$ 
D)  $7 \log _ { 2 } x - \log _ { 2 } ( x + 5 )$ 
A)  $\log _ { 2 } ( x + 5 ) - 7 \log _ { 2 } x$ 
B)  $\log _ { 2 } ( x + 5 ) + 7 \log _ { 2 } x$ 
C)  $\log _ { 2 } ( x + 5 ) - \log _ { 2 } x$ 
D)  $7 \log _ { 2 } x - \log _ { 2 } ( x + 5 )$

Question 12

Find functions f and g so that f ° g = H.
-$$H ( x ) = \sqrt [ 3 ] { x + 1 }$$

Accepted Answer

A)  $f ( x ) = \sqrt { x } ; g ( x ) = x + 1$ 
B)  $f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = x + 1$ 
C)  $f ( x ) = x + 1 ; g ( x ) = \sqrt [ 3 ] { x }$ 
D)  $f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = 1$ 
A)  $f ( x ) = \sqrt { x } ; g ( x ) = x + 1$ 
B)  $f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = x + 1$ 
C)  $f ( x ) = x + 1 ; g ( x ) = \sqrt [ 3 ] { x }$ 
D)  $f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = 1$

Question 13

Write the word or phrase that best completes each statement or answers the question.
-A company with load machinery needs to cut its sound intensity to 72% of its original level. By how many
decibels should the loudness be reduced?

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

The function f is one-to-one. Find its inverse.
-$$f ( x ) = \frac { 4 } { 7 x - 5 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { 4 + 5 x } { 7 x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { - 5 x - 4 } { 7 x }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 7 \mathrm { x } - 5 } { 4 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 + 5 \mathrm { y } } { 7 \mathrm { y } }$ 
A)  $f ^ { - 1 } ( x ) = \frac { 4 + 5 x } { 7 x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { - 5 x - 4 } { 7 x }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 7 \mathrm { x } - 5 } { 4 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 + 5 \mathrm { y } } { 7 \mathrm { y } }$

Question 15

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$\log _ { 5 } ( x + 4 ) = 3$

Accepted Answer

A)  $\{ 121 \}$ 
B)  $\{ 129 \}$ 
C)  $\{ 247 \}$ 
D)  $\{ 239 \}$ 
A)  $\{ 121 \}$ 
B)  $\{ 129 \}$ 
C)  $\{ 247 \}$ 
D)  $\{ 239 \}$

Question 16

Choose the one alternative that best completes the statement or answers the question.
The graph of a logarithmic function is shown. Select the function which matches the graph.
-

Accepted Answer

A)  $f ( x ) = \log _ { 5 } x$ 
B)  $f ( x ) = \log _ { 5 } ( x - 1 )$ 
C)  $f ( x ) = \log _ { 5 } x - 1$ 
D)  $f ( x ) = \log _ { 5 } ( x + 1 )$ 
A)  $f ( x ) = \log _ { 5 } x$ 
B)  $f ( x ) = \log _ { 5 } ( x - 1 )$ 
C)  $f ( x ) = \log _ { 5 } x - 1$ 
D)  $f ( x ) = \log _ { 5 } ( x + 1 )$

Question 17

Choose the one alternative that best completes the statement or answers the question.
Find the domain of the composite function f ° g.
-$$f ( x ) = \frac { 6 } { x + 1 } ; \quad g ( x ) = x + 2$$

Accepted Answer

A)  $\{ x \mid x \neq - 3 \}$ 
B)  $\{ x \mid x$ is any real number $\}$ 
C)  $\{ x \mid x \neq - 1 \}$ 
D)  $\{ x \mid x \neq - 1 , x \neq - 2 \}$ 
A)  $\{ x \mid x \neq - 3 \}$ 
B)  $\{ x \mid x$ is any real number $\}$ 
C)  $\{ x \mid x \neq - 1 \}$ 
D)  $\{ x \mid x \neq - 1 , x \neq - 2 \}$

Question 18

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places.
-$\log _ { \sqrt { 5 } } 215.3$

Accepted Answer

A)  $6.68$ 
B)  $3.34$ 
C)  $0.15$ 
D)  $0.35$ 
A)  $6.68$ 
B)  $3.34$ 
C)  $0.15$ 
D)  $0.35$

Question 19

Use a calculator to find the natural logarithm correct to four decimal places.
-$\ln 49,800,000$

Accepted Answer

A)  $17.7235$ 
B)  $7.6972$ 
C)  $0.0563$ 
D)  $6.2106$ 
A)  $17.7235$ 
B)  $7.6972$ 
C)  $0.0563$ 
D)  $6.2106$

Question 20

Solve the equation.
-$$4 ^ { - x } = \frac { 1 } { 16 }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\{ 2 \}$ 
C)  $\{ - 2 \}$ 
D)  $\left\{ \frac { 1 } { 4 } \right\}$ 
A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\{ 2 \}$ 
C)  $\{ - 2 \}$ 
D)  $\left\{ \frac { 1 } { 4 } \right\}$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\ln \sqrt { x + 2 } = 4$

Find the exact value of the logarithmic expression. - $\log _ { 4 } 16$

Find functions f and g so that f ° g = H. - $H ( x ) = | 9 x + 3 |$

Find the domain of the function. - $f ( x ) = \log _ { 6 } \left( 36 - x ^ { 2 } \right)$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\log _ { 6 } \left( x ^ { 2 } - 5 x \right) = 1$

The function f is one-to-one. Find its inverse. - $f ( x ) = 2 x$

For the given functions f and g, find the requested composite function. - $f ( x ) = \frac { x - 10 } { 2 } , g ( x ) = 2 x + 10 ; \quad$ Find $( g \circ f ) ( x )$

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln 200$

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 2 } \left( \frac { x + 5 } { x ^ { 7 } } \right)$

Find functions f and g so that f ° g = H. - $H ( x ) = \sqrt [ 3 ] { x + 1 }$

Write the word or phrase that best completes each statement or answers the question. -A company with load machinery needs to cut its sound intensity to 72% of its original level. By how many decibels should the loudness be reduced?

The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 4 } { 7 x - 5 }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\log _ { 5 } ( x + 4 ) = 3$

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Choose the one alternative that best completes the statement or answers the question. Find the domain of the composite function f ° g. - $f ( x ) = \frac { 6 } { x + 1 } ; \quad g ( x ) = x + 2$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { \sqrt { 5 } } 215.3$

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln 49,800,000$

Solve the equation. - $4 ^ { - x } = \frac { 1 } { 16 }$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 4: Exponential and Logarithmic Functions

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - ln⁡x+2=4\ln \sqrt { x + 2 } = 4lnx+2​=4

Find the exact value of the logarithmic expression. - log⁡416\log _ { 4 } 16log4​16

Find functions f and g so that f ° g = H. - H(x)=∣9x+3∣H ( x ) = | 9 x + 3 |H(x)=∣9x+3∣

Find the domain of the function. - f(x)=log⁡6(36−x2)f ( x ) = \log _ { 6 } \left( 36 - x ^ { 2 } \right)f(x)=log6​(36−x2)

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - log⁡6(x2−5x)=1\log _ { 6 } \left( x ^ { 2 } - 5 x \right) = 1log6​(x2−5x)=1

The function f is one-to-one. Find its inverse. - f(x)=2xf ( x ) = 2 xf(x)=2x

For the given functions f and g, find the requested composite function. - f(x)=x−102,g(x)=2x+10;f ( x ) = \frac { x - 10 } { 2 } , g ( x ) = 2 x + 10 ; \quadf(x)=2x−10​,g(x)=2x+10; Find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

Use a calculator to find the natural logarithm correct to four decimal places. - ln⁡200\ln 200ln200

Write as the sum and/or difference of logarithms. Express powers as factors. - log⁡2(x+5x7)\log _ { 2 } \left( \frac { x + 5 } { x ^ { 7 } } \right)log2​(x7x+5​)

Find functions f and g so that f ° g = H. - H(x)=x+13H ( x ) = \sqrt [ 3 ] { x + 1 }H(x)=3x+1​