Question 1

Write the equation in its equivalent exponential form.
-$\log _ { 5 } x = 2$

Accepted Answer

A)  $5 ^ { 2 } = x$ 
B)  $25 = x$ 
C)  $5 x = 2$ 
D)  $x ^ { 2 } = 5$ x 
A)  $5 ^ { 2 } = x$ 
B)  $25 = x$ 
C)  $5 x = 2$ 
D)  $x ^ { 2 } = 5$ x

Question 2

Graph the function
-Use the graph of $f ( x ) = 4 ^ { x }$ to obtain the graph of $g ( x ) = \frac { 1 } { 4 } \cdot 4 ^ { x }$.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 3

Solve the problem.
-Cindy will require $\$ 14,000$ in 2 years to return to college to get an MBA degree. How much money should she ask her parents for now so that, if she invests it at $11 \%$ compounded continuously, she will have enough for school? (Round your answer to the nearest dollar.)

Accepted Answer

A)  $\$ 11,235$ 
B)  $\$ 11,363$ 
C)  $\$ 17,445$ 
D)  $\$ 9017$ 
A)  $\$ 11,235$ 
B)  $\$ 11,363$ 
C)  $\$ 17,445$ 
D)  $\$ 9017$

Question 4

Approximate the number using a calculator. Round your answer to three decimal places.
-$4 ^ { \pi }$

Accepted Answer

A)  $77.880$ 
B)  $97.409$ 
C)  $12.566$ 
D)  $36.462$ 
A)  $77.880$ 
B)  $97.409$ 
C)  $12.566$ 
D)  $36.462$

Question 5

Evaluate the expression without using a calculator.
-The function $\mathrm { f } ( \mathrm { x } ) = 1 + 1.6 \ln ( \mathrm { x } + 1 )$ models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where $\mathrm { x }$ is the number of consecutive days the basketball player has practiced for two hours. After 147 days of practice, what is the average number of consecutive free throws the basketball player makes?

Accepted Answer

A)  9 consecutive free throws 
B)  10 consecutive free throws 
C)  12 consecutive free throws 
D)  13 consecutive free throws 
A)  9 consecutive free throws 
B)  10 consecutive free throws 
C)  12 consecutive free throws 
D)  13 consecutive free throws

Question 6

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log \left[ \frac { 4 x ^ { 3 } \sqrt [ 4 ] { 3 - x } } { 10 ( x + 3 ) ^ { 2 } } \right]$

Accepted Answer

A)  $\log 4 + 3 \log x + \frac { 1 } { 4 } \log ( 3 - x ) - \log 10 - 2 \log ( x + 3 )$ 
B)  $\log 4 + \log x ^ { 3 } + \log ( 3 - x ) ^ { 1 / 4 } - \log 10 - \log ( x + 3 ) ^ { 2 }$ 
C)  $\log \left( 4 x ^ { 3 } \sqrt [ 4 ] { 3 - x } \right) - \log \left( 10 ( x + 3 ) ^ { 2 } \right)$ 
D)  $\log 4 + 3 \log x + \frac { 1 } { 4 } \log ( 3 - x ) - \log 10 + 2 \log ( x + 3 )$ 
A)  $\log 4 + 3 \log x + \frac { 1 } { 4 } \log ( 3 - x ) - \log 10 - 2 \log ( x + 3 )$ 
B)  $\log 4 + \log x ^ { 3 } + \log ( 3 - x ) ^ { 1 / 4 } - \log 10 - \log ( x + 3 ) ^ { 2 }$ 
C)  $\log \left( 4 x ^ { 3 } \sqrt [ 4 ] { 3 - x } \right) - \log \left( 10 ( x + 3 ) ^ { 2 } \right)$ 
D)  $\log 4 + 3 \log x + \frac { 1 } { 4 } \log ( 3 - x ) - \log 10 + 2 \log ( x + 3 )$

Question 7

Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
-Find the accumulated value of an investment of $5000 at 5% compounded monthly for 8 years.

Accepted Answer

A)  $7452.93 
B)  $12,911.25 
C)  $9093.60 
D)  $8060.16 
A)  $7452.93 
B)  $12,911.25 
C)  $9093.60 
D)  $8060.16

Question 8

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-

Accepted Answer

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

Question 9

Solve the equation by expressing each side as a power of the same base and then equating exponents.
-$$27 ^ { x } = \frac { 1 } { \sqrt { 3 } }$$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
B)  $\left\{ \frac { 1 } { 6 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 3 } \right\}$ 
D)  $\{ - 3 \}$ 
A)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
B)  $\left\{ \frac { 1 } { 6 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 3 } \right\}$ 
D)  $\{ - 3 \}$

Question 10

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
-$$\log _ { 2 } ( 7 x - 2 ) = \log _ { 2 } ( 2 x + 5 )$$

Accepted Answer

A)  $\left\{ \frac { 7 } { 5 } \right\}$ 
B)  $\left\{ \frac { 3 } { 5 } \right\}$ 
C)  $\{ 3 \}$ 
D)  $\varnothing$ 
A)  $\left\{ \frac { 7 } { 5 } \right\}$ 
B)  $\left\{ \frac { 3 } { 5 } \right\}$ 
C)  $\{ 3 \}$ 
D)  $\varnothing$

Question 11

Evaluate the expression without using a calculator.
-${ } _ { 3 } \log _ { 3 } 18$

Accepted Answer

A)  18 
B)  3 
C)  21 
D)  $\log _ { 3 } 18$ 
A)  18 
B)  3 
C)  21 
D)  $\log _ { 3 } 18$

Question 12

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm
whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$$\frac { 1 } { 4 } \left( \log _ { 8 } x + \log _ { 8 } y \right) - 6 \log 8 ( x + 1 )$$

Accepted Answer

A)  $\log _ { 8 } \frac { \sqrt [ 4 ] { x y } } { ( x + 1 ) ^ { 6 } }$ 
B)  $\log 8 \frac { \sqrt [ 4 ] { x + y } } { ( x + 1 ) ^ { 6 } }$ 
C)  $\log 8 \frac { \sqrt [ 4 ] { x y } } { 6 ( x + 1 ) }$ 
D)  $\log _ { 8 } \frac { \sqrt [ 4 ] { x } + \sqrt [ 4 ] { y } } { ( x + 1 ) ^ { 6 } }$ 
A)  $\log _ { 8 } \frac { \sqrt [ 4 ] { x y } } { ( x + 1 ) ^ { 6 } }$ 
B)  $\log 8 \frac { \sqrt [ 4 ] { x + y } } { ( x + 1 ) ^ { 6 } }$ 
C)  $\log 8 \frac { \sqrt [ 4 ] { x y } } { 6 ( x + 1 ) }$ 
D)  $\log _ { 8 } \frac { \sqrt [ 4 ] { x } + \sqrt [ 4 ] { y } } { ( x + 1 ) ^ { 6 } }$

Question 13

Solve the equation by expressing each side as a power of the same base and then equating exponents.
-$$3 ^ { ( 3 x - 6 ) } = 27$$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 1 } { 9 } \right\}$ 
C)  $\{ 9 \}$ 
D)  $\{ - 3 \}$ 
A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 1 } { 9 } \right\}$ 
C)  $\{ 9 \}$ 
D)  $\{ - 3 \}$

Question 14

Approximate the number using a calculator. Round your answer to three decimal places.
-$6 ^{\sqrt { 2 }}$

Accepted Answer

A)  $12.603$ 
B)  $8.485$ 
C)  $8.000$ 
D)  $18.000$ 
A)  $12.603$ 
B)  $8.485$ 
C)  $8.000$ 
D)  $18.000$

Question 15

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 6 } \sqrt [ 5 ] { \frac { x ^ { 2 } y } { 36 } }$

Accepted Answer

A)  $\frac { 2 } { 5 } \log _ { 6 } x + \frac { 1 } { 5 } \log _ { 6 } y - \frac { 2 } { 5 }$ 
B)  $\frac { 1 } { 5 } \left( \log _ { 6 } x ^ { 2 } + \log _ { 6 } y - 2 \right)$ 
C)  $\frac { 1 } { 5 } \left( \log _ { 6 } x ^ { 2 } y - \log _ { 6 } 36 \right)$ 
D)  $\frac { 2 } { 5 } \log _ { 6 } x - \frac { 1 } { 5 } \log 6 y + \frac { 2 } { 5 }$ 
A)  $\frac { 2 } { 5 } \log _ { 6 } x + \frac { 1 } { 5 } \log _ { 6 } y - \frac { 2 } { 5 }$ 
B)  $\frac { 1 } { 5 } \left( \log _ { 6 } x ^ { 2 } + \log _ { 6 } y - 2 \right)$ 
C)  $\frac { 1 } { 5 } \left( \log _ { 6 } x ^ { 2 } y - \log _ { 6 } 36 \right)$ 
D)  $\frac { 2 } { 5 } \log _ { 6 } x - \frac { 1 } { 5 } \log 6 y + \frac { 2 } { 5 }$

Question 16

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 17 } \left( \frac { \sqrt [ 2 ] { 5 } } { y ^ { 2 } x } \right)$

Accepted Answer

A)  $\frac { 1 } { 2 } \log _ { 17 } 5 - 2 \log _ { 17 } y - \log _ { 17 } x$ 
B)  $2 \log _ { 17 } 5 - 2 \log _ { 17 } y - \log _ { 17 } 2$ 
C)  $\frac { 1 } { 2 } \log _ { 17 } 5 - 2 \log _ { 17 } \mathrm { y } - 2 \log _ { 17 } \mathrm { x }$ 
D)  $\log _ { 17 } 5 - \log _ { 17 } y - \log _ { 17 } x$ 
A)  $\frac { 1 } { 2 } \log _ { 17 } 5 - 2 \log _ { 17 } y - \log _ { 17 } x$ 
B)  $2 \log _ { 17 } 5 - 2 \log _ { 17 } y - \log _ { 17 } 2$ 
C)  $\frac { 1 } { 2 } \log _ { 17 } 5 - 2 \log _ { 17 } \mathrm { y } - 2 \log _ { 17 } \mathrm { x }$ 
D)  $\log _ { 17 } 5 - \log _ { 17 } y - \log _ { 17 } x$

Question 17

Graph the function.
-Use the graph of $f ( x ) = \log x$ to obtain the graph of $g ( x ) = \log x - 2$.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 18

Evaluate or simplify the expression without using a calculator.
-$\ln 1$

Accepted Answer

A)  0 
B)  1 
C)  e 
D)  $- 1$ 
A)  0 
B)  1 
C)  e 
D)  $- 1$

Question 19

Solve the problem.
-The population of a particular country was 22 million in 1985 ; in 2000 , it was 31 million. The exponential growth function $\mathrm { A } = 22 \mathrm { e } ^ { \mathrm { kt } }$ describes the population of this country t years after 1985 . Use the fact that 15 years after 1985 the population increased by 9 million to find $k$ to three decimal places.

Accepted Answer

A)  $0.023$ 
B)  $0.146$ 
C)  $0.435$ 
D)  $0.033$ 
A)  $0.023$ 
B)  $0.146$ 
C)  $0.435$ 
D)  $0.033$

Question 20

Find the domain of the logarithmic function.
-$$f ( x ) = \log _ { 7 } ( x + 3 )$$

Accepted Answer

A)  $( - 3 , \infty )$ 
B)  $( 7 , \infty )$ 
C)  $( 3 , \infty )$ 
D)  $( - \infty , 0 )$ or $( 0 , \infty )$ 
A)  $( - 3 , \infty )$ 
B)  $( 7 , \infty )$ 
C)  $( 3 , \infty )$ 
D)  $( - \infty , 0 )$ or $( 0 , \infty )$

Write the equation in its equivalent exponential form. - $\log _ { 5 } x = 2$

Graph the function -Use the graph of $f ( x ) = 4 ^ { x }$ to obtain the graph of $g ( x ) = \frac { 1 } { 4 } \cdot 4 ^ { x }$ . $Graph the function -Use the graph of f ( x ) = 4 ^ { x } to obtain the graph of g ( x ) = \frac { 1 } { 4 } \cdot 4 ^ { x } .$

Solve the problem. -Cindy will require $\$ 14,000$ in 2 years to return to college to get an MBA degree. How much money should she ask her parents for now so that, if she invests it at $11 \%$ compounded continuously, she will have enough for school? (Round your answer to the nearest dollar.)

Approximate the number using a calculator. Round your answer to three decimal places. - $4 ^ { \pi }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log \left[ \frac { 4 x ^ { 3 } \sqrt [ 4 ] { 3 - x } } { 10 ( x + 3 ) ^ { 2 } } \right]$

Use the compound interest formulas A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$ -Find the accumulated value of an investment of $5000 at 5% compounded monthly for 8 years.

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Solve the equation by expressing each side as a power of the same base and then equating exponents. - $27 ^ { x } = \frac { 1 } { \sqrt { 3 } }$

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log _ { 2 } ( 7 x - 2 ) = \log _ { 2 } ( 2 x + 5 )$

Evaluate the expression without using a calculator. - ${ } _ { 3 } \log _ { 3 } 18$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\frac { 1 } { 4 } \left( \log _ { 8 } x + \log _ { 8 } y \right) - 6 \log 8 ( x + 1 )$

Solve the equation by expressing each side as a power of the same base and then equating exponents. - $3 ^ { ( 3 x - 6 ) } = 27$

Approximate the number using a calculator. Round your answer to three decimal places. - $6 ^{\sqrt { 2 }}$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 6 } \sqrt [ 5 ] { \frac { x ^ { 2 } y } { 36 } }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 17 } \left( \frac { \sqrt [ 2 ] { 5 } } { y ^ { 2 } x } \right)$

Graph the function. -Use the graph of $f ( x ) = \log x$ to obtain the graph of $g ( x ) = \log x - 2$ . $Graph the function. -Use the graph of f ( x ) = \log x to obtain the graph of g ( x ) = \log x - 2 .$

Evaluate or simplify the expression without using a calculator. - $\ln 1$

Find the domain of the logarithmic function. - $f ( x ) = \log _ { 7 } ( x + 3 )$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 4: Exponential and Logarithmic Functions

Write the equation in its equivalent exponential form. - log⁡5x=2\log _ { 5 } x = 2log5​x=2

Graph the function -Use the graph of f(x)=4xf ( x ) = 4 ^ { x }f(x)=4x to obtain the graph of g(x)=14⋅4xg ( x ) = \frac { 1 } { 4 } \cdot 4 ^ { x }g(x)=41​⋅4x .

Approximate the number using a calculator. Round your answer to three decimal places. - 4π4 ^ { \pi }4π