Question 1

Solve the exponential equation. Express the solution set in terms of natural logarithms.
-$$7 ^ { x } = 15$$

Accepted Answer

A)  $1.39$ 
B)  $5.27$ 
C)  $0.72$ 
D)  $0.99$ 
A)  $1.39$ 
B)  $5.27$ 
C)  $0.72$ 
D)  $0.99$ A

Question 2

Graph the function
-Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 ^ { x - 4 }$.

Accepted Answer

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

Question 3

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$$\log _ { 3 } x ^ { 6 }$$

Accepted Answer

A)  $6 \log _ { 3 } x$ 
B)  $3 \log _ { 6 } x$ 
C)  $3 \log x$ 
D)  $6 \log _ { 3 } x ^ { 6 }$ 
A)  $6 \log _ { 3 } x$ 
B)  $3 \log _ { 6 } x$ 
C)  $3 \log x$ 
D)  $6 \log _ { 3 } x ^ { 6 }$ A

Question 4

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.
-$2 \log x - \log 6 = \log 96$

Accepted Answer

A)  $\{ 24 \}$ 
B)  $\{ - 24 \}$ 
C)  $\{ 24 , - 24 \}$ 
D)  $\{ 288 \}$ 
A)  $\{ 24 \}$ 
B)  $\{ - 24 \}$ 
C)  $\{ 24 , - 24 \}$ 
D)  $\{ 288 \}$

Question 5

Evaluate the expression without using a calculator.
-$\mathrm { e } ^ { \ln 6 \mathrm { x } ^ { 2 } }$

Accepted Answer

A)  $6 x ^ { 2 }$ 
B)  $e ^ { 6 x ^ { 2 } }$ 
C)  $\ln 6 x ^ { 2 }$ 
D)  2 
A)  $6 x ^ { 2 }$ 
B)  $e ^ { 6 x ^ { 2 } }$ 
C)  $\ln 6 x ^ { 2 }$ 
D)  2

Question 6

Evaluate or simplify the expression without using a calculator.
-$\ln \sqrt [ 8 ] { \mathrm { e } }$

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  $\frac { e } { 8 }$ 
C)  8 
D)  $8 \mathrm { e }$ 
A)  $\frac { 1 } { 8 }$ 
B)  $\frac { e } { 8 }$ 
C)  8 
D)  $8 \mathrm { e }$

Question 7

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 3 } 3 ^ { - 4 }$

Accepted Answer

A)  $- 4 \log _ { 3 } 3$ 
B)  $3 \log _ { 4 } 3$ 
C)  $- 12 \log 3$ 
D)  $3 \log _ { 3 } 4$ 
A)  $- 4 \log _ { 3 } 3$ 
B)  $3 \log _ { 4 } 3$ 
C)  $- 12 \log 3$ 
D)  $3 \log _ { 3 } 4$

Question 8

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places
-$\log _ { 20 } 371$

Accepted Answer

A)  $1.9749$ 
B)  $0.5064$ 
C)  $3.8704$ 
D)  $1.2683$ 
A)  $1.9749$ 
B)  $0.5064$ 
C)  $3.8704$ 
D)  $1.2683$

Question 9

The graph of a logarithmic function is given. Select the function for the graph from the options.
-

Accepted Answer

A)  $f ( x ) = \log _ { 3 } ( - x )$ 
B)  $f ( x ) = - \log _ { 3 } x$ 
C)  $f ( x ) = 1 - \log _ { 3 } x$ 
D)  $f ( x ) = \log _ { 3 } x$ 
A)  $f ( x ) = \log _ { 3 } ( - x )$ 
B)  $f ( x ) = - \log _ { 3 } x$ 
C)  $f ( x ) = 1 - \log _ { 3 } x$ 
D)  $f ( x ) = \log _ { 3 } x$

Question 10

Solve the exponential equation. Express the solution set in terms of natural logarithms.
-$$e ^ { 5 x - 10 } - 4 = 1456$$

Accepted Answer

A)  $3.46$ 
B)  $2.63$ 
C)  $1.46$ 
D)  $0.63$ 
A)  $3.46$ 
B)  $2.63$ 
C)  $1.46$ 
D)  $0.63$

Question 11

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 4 } \left( \frac { \sqrt { x } } { 16 } \right)$

Accepted Answer

A)  $\frac { 1 } { 2 } \log _ { 4 } x - 2$ 
B)  $8 - \frac { 1 } { 2 } \log _ { 4 } x$ 
C)  $\log _ { 4 } x - 2$ 
D)  $- 2 \log _ { 4 } x$ 
A)  $\frac { 1 } { 2 } \log _ { 4 } x - 2$ 
B)  $8 - \frac { 1 } { 2 } \log _ { 4 } x$ 
C)  $\log _ { 4 } x - 2$ 
D)  $- 2 \log _ { 4 } x$

Question 12

Find the domain of the logarithmic function.
-$$f ( x ) = \ln \left( \frac { 1 } { x - 6 } \right)$$

Accepted Answer

A)  $( 6 , \infty )$ 
B)  $( - 6 , \infty )$ 
C)  $( 0 , \infty )$ 
D)  $( 1 , \infty )$ 
A)  $( 6 , \infty )$ 
B)  $( - 6 , \infty )$ 
C)  $( 0 , \infty )$ 
D)  $( 1 , \infty )$

Question 13

Write the equation in its equivalent logarithmic form.
-$$9 ^ { x } = 729$$

Accepted Answer

A)  $\log _ { 9 } 729 = \mathrm { x }$ 
B)  $\log _ { x } 729 = 9$ 
C)  $\log _ { 729 } 9 = \mathrm { x }$ 
D)  $\log _ { 729 } x = 9$ 
A)  $\log _ { 9 } 729 = \mathrm { x }$ 
B)  $\log _ { x } 729 = 9$ 
C)  $\log _ { 729 } 9 = \mathrm { x }$ 
D)  $\log _ { 729 } x = 9$

Question 14

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.
-$\log 3 x = \log 5 + \log ( x - 2 )$

Accepted Answer

A)  $\{ 5 \}$ 
B)  $\left\{ \frac { 3 } { 2 } \right\}$ 
C)  $\{ - 5 \}$ 
D)  $\left\{ - \frac { 5 } { 4 } \right\}$ 
A)  $\{ 5 \}$ 
B)  $\left\{ \frac { 3 } { 2 } \right\}$ 
C)  $\{ - 5 \}$ 
D)  $\left\{ - \frac { 5 } { 4 } \right\}$

Question 15

Solve the equation by expressing each side as a power of the same base and then equating exponents.
-$$10 ( x - 3 ) / 2 = \sqrt { 10 }$$

Accepted Answer

A)  $\{ 4 \}$ 
B)  $\{ 7 \}$ 
C)  $\{ 5 \}$ 
D)  $\left\{ \frac { 11 } { 3 } \right\}$ 
A)  $\{ 4 \}$ 
B)  $\{ 7 \}$ 
C)  $\{ 5 \}$ 
D)  $\left\{ \frac { 11 } { 3 } \right\}$

Question 16

Solve the problem.
-The $\mathrm { pH }$ of a solution ranges from 0 to 14 . An acid has a pH less than 7 . Pure water is neutral and has a pH of 7 . The $\mathrm { pH }$ of a solution is given by $\mathrm { pH } = - \log \mathrm { x }$ where $\mathrm { x }$ represents the concentration of the hydrogen ions in the solution in moles per liter. Find the hydrogen ion concentration if the $\mathrm { pH } = 8.4$.

Accepted Answer

A)  $3.98 \times 10 ^ { - 9 }$ 
B)  $3.98 \times 10^{ - 8}$ 
C)  $2.51 \times 10 ^ { - 8 }$ 
D)  $2.51 \times 10 ^ { - 9 }$ 
A)  $3.98 \times 10 ^ { - 9 }$ 
B)  $3.98 \times 10^{ - 8}$ 
C)  $2.51 \times 10 ^ { - 8 }$ 
D)  $2.51 \times 10 ^ { - 9 }$

Question 17

Solve the exponential equation. Express the solution set in terms of natural logarithms.
-$$4 ^ { x + 4 } = 5 ^ { 2 x + 5 }$$

Accepted Answer

A)  $\left\{ \frac { 5 \ln 5 - 4 \ln 4 } { \ln 4 - 2 \ln 5 } \right\}$ 
B)  $\left\{ \ln \left[ \frac { 5 ^ { 5 } } { 4 ^ { 4 } } - \frac { 4 } { 5 ^ { 2 } } \right] \right\}$ 
C)  $\{ \ln 5 - \ln 4 \}$ 
D)  $\{ 7 \ln 5 - 5 \ln 4$ Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 
A)  $\left\{ \frac { 5 \ln 5 - 4 \ln 4 } { \ln 4 - 2 \ln 5 } \right\}$ 
B)  $\left\{ \ln \left[ \frac { 5 ^ { 5 } } { 4 ^ { 4 } } - \frac { 4 } { 5 ^ { 2 } } \right] \right\}$ 
C)  $\{ \ln 5 - \ln 4 \}$ 
D)  $\{ 7 \ln 5 - 5 \ln 4$ Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

Question 18

Evaluate the expression without using a calculator.
-$\log _ { 9 } 9$

Accepted Answer

A)  1 
B)  9 
C)  $\frac { 1 } { 9 }$ 
D)  0 
A)  1 
B)  9 
C)  $\frac { 1 } { 9 }$ 
D)  0

Question 19

Evaluate or simplify the expression without using a calculator.
-$\log 10 ^ { 2 }$

Accepted Answer

A)  2 
B)  10 
C)  $\log 2$ 
D)  $10 ^ { 2 }$ 
A)  2 
B)  10 
C)  $\log 2$ 
D)  $10 ^ { 2 }$

Question 20

Approximate the number using a calculator. Round your answer to three decimal places.
-$\mathrm { e } ^ { 3.4 }$

Accepted Answer

A)  $29.964$ 
B)  $9.242$ 
C)  $27.843$ 
D)  $30.264$ 
A)  $29.964$ 
B)  $9.242$ 
C)  $27.843$ 
D)  $30.264$

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $7 ^ { x } = 15$

Graph the function -Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 ^ { x - 4 }$ . $Graph the function -Use the graph of f ( x ) = 2 ^ { x } to obtain the graph of g ( x ) = 2 ^ { x - 4 } .$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } x ^ { 6 }$

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. - $2 \log x - \log 6 = \log 96$

Evaluate the expression without using a calculator. - $\mathrm { e } ^ { \ln 6 \mathrm { x } ^ { 2 } }$

Evaluate or simplify the expression without using a calculator. - $\ln \sqrt [ 8 ] { \mathrm { e } }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } 3 ^ { - 4 }$

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places - $\log _ { 20 } 371$

The graph of a logarithmic function is given. Select the function for the graph from the options. -

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $e ^ { 5 x - 10 } - 4 = 1456$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 4 } \left( \frac { \sqrt { x } } { 16 } \right)$

Find the domain of the logarithmic function. - $f ( x ) = \ln \left( \frac { 1 } { x - 6 } \right)$

Write the equation in its equivalent logarithmic form. - $9 ^ { x } = 729$

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. - $\log 3 x = \log 5 + \log ( x - 2 )$

Solve the equation by expressing each side as a power of the same base and then equating exponents. - $10 ( x - 3 ) / 2 = \sqrt { 10 }$

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $4 ^ { x + 4 } = 5 ^ { 2 x + 5 }$

Evaluate the expression without using a calculator. - $\log _ { 9 } 9$

Evaluate or simplify the expression without using a calculator. - $\log 10 ^ { 2 }$

Approximate the number using a calculator. Round your answer to three decimal places. - $\mathrm { e } ^ { 3.4 }$

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

Solve the exponential equation. Express the solution set in terms of natural logarithms. - 7x=157 ^ { x } = 157x=15

Graph the function -Use the graph of f(x)=2xf ( x ) = 2 ^ { x }f(x)=2x to obtain the graph of g(x)=2x−4g ( x ) = 2 ^ { x - 4 }g(x)=2x−4 .

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡3x6\log _ { 3 } x ^ { 6 }log3​x6

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. - 2log⁡x−log⁡6=log⁡962 \log x - \log 6 = \log 962logx−log6=log96

Evaluate the expression without using a calculator. - eln⁡6x2\mathrm { e } ^ { \ln 6 \mathrm { x } ^ { 2 } }eln6x2

Evaluate or simplify the expression without using a calculator. - ln⁡e8\ln \sqrt [ 8 ] { \mathrm { e } }ln8e​

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡33−4\log _ { 3 } 3 ^ { - 4 }log3​3−4

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places - log⁡20371\log _ { 20 } 371log20​371