Question 1

Write the exponential equation in logarithmic form.  $2 ^ { 3 } = 8$

Accepted Answer

A)  $\log _ { 8 } 2 = 3$ 
B)  $\log _ { 2 } 8 = 3$ 
C)  $\log _ { 8 } 2 = - 3$ 
D)  $\log _ { 2 } 3 = 8$ 
E)  $\log _ { 2 } 8 = \frac { 1 } { 3 }$ 
A)  $\log _ { 8 } 2 = 3$ 
B)  $\log _ { 2 } 8 = 3$ 
C)  $\log _ { 8 } 2 = - 3$ 
D)  $\log _ { 2 } 3 = 8$ 
E)  $\log _ { 2 } 8 = \frac { 1 } { 3 }$ B

Question 2

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places.  $x = 25.5$

Accepted Answer

A) -1.407 
B) 1.407 
C) 0.711 
D) 0.039 
E) -0.711 
A) -1.407 
B) 1.407 
C) 0.711 
D) 0.039 
E) -0.711 B

Question 3

Graph the function using translations.  $f ( x ) = e ^ { x + 1 } + 2$

Accepted Answer

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

Question 4

Rewrite the logarithm as a ratio of common logarithms. 
Log2.7 x

Accepted Answer

A)  $\frac { \log 2.7 } { \log x }$ 
B)  $\frac { \log x } { \log 2.7 }$ 
C)  $\log \frac { x } { 2.7 }$ 
D)  $\log 2.7 x$ 
E) None of these 
A)  $\frac { \log 2.7 } { \log x }$ 
B)  $\frac { \log x } { \log 2.7 }$ 
C)  $\log \frac { x } { 2.7 }$ 
D)  $\log 2.7 x$ 
E) None of these

Question 5

Condense the expression log4 x + log4 3 to the logarithm of a single term.

Accepted Answer

A) log4 2x 
B) log4 3x 
C) log4 x3 
D) log(3x)4 
E) log4 (x + 3) 
A) log4 2x 
B) log4 3x 
C) log4 x3 
D) log(3x)4 
E) log4 (x + 3)

Question 6

Use the properties of logarithms to rewrite and simplify the logarithmic expression. ​
Log2 (42 · 74)
​

Accepted Answer

A) 4 + 9 log2 4 
B) 9 + 4 log2 4 
C) 2 + 2 log2 7 
D) 4 + 4 log2 7 
E) 2 + 4 log2 7 
A) 4 + 9 log2 4 
B) 9 + 4 log2 4 
C) 2 + 2 log2 7 
D) 4 + 4 log2 7 
E) 2 + 4 log2 7

Question 7

Solve the exponential equation algebraically.Approximate the result to three decimal places.   $1000 e ^ { - 4 x } = 75$

Accepted Answer

A)  $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 2.648$ 
B)  $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx - 1.352$ 
C)  $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 1.648$ 
D)  $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 0.648$ 
E)  $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx - 0.352$ 
A)  $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 2.648$ 
B)  $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx - 1.352$ 
C)  $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 1.648$ 
D)  $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 0.648$ 
E)  $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx - 0.352$

Question 8

Evaluate the function at the indicated value of $x = 281 ^ { 5 }$ .  $g ( x ) = \log _ { 281 } x$

Accepted Answer

A) -5 
B)  $\frac { 1 } { 5 }$ 
C)  $- \frac { 1 } { 5 }$ 
D) 5 
E) 0 
A) -5 
B)  $\frac { 1 } { 5 }$ 
C)  $- \frac { 1 } { 5 }$ 
D) 5 
E) 0

Question 9

Solve for x.   $6 ^ { x } = 36$

Accepted Answer

A) 8 
B) 2 
C) -2 
D) -6 
E) 6 
A) 8 
B) 2 
C) -2 
D) -6 
E) 6

Question 10

Solve the exponential equation algebraically.Approximate the result to three decimal places. 
 $- 22 + 4 e ^ { x } = 13$

Accepted Answer

A)  $\ln \frac { 35 } { 4 } \approx 1.169$ 
B)  $\ln \frac { 35 } { 4 } \approx 4.169$ 
C)  $\ln \frac { 35 } { 4 } \approx 2.169$ 
D)  $\ln \frac { 35 } { 4 } \approx 0.169$ 
E)  $\ln \frac { 35 } { 4 } \approx 3.169$ 
A)  $\ln \frac { 35 } { 4 } \approx 1.169$ 
B)  $\ln \frac { 35 } { 4 } \approx 4.169$ 
C)  $\ln \frac { 35 } { 4 } \approx 2.169$ 
D)  $\ln \frac { 35 } { 4 } \approx 0.169$ 
E)  $\ln \frac { 35 } { 4 } \approx 3.169$

Question 11

Evaluate the function at the indicated value of $x$ .Round your result to three decimal places. 
Function
Value $f ( x ) = 200 ( 1.3 ) ^ { 12 x }$ $x = 14$

Accepted Answer

A)  $2.504 \times 10 ^ { 2 }$ 
B)  $4.368 \times 10 ^ { 4 }$ 
C)  $3.048 \times 10 ^ { 36 }$ 
D)  $1.183 \times 10 ^ { 2 }$ 
E)  $2.777 \times 10 ^ { 21 }$ 
A)  $2.504 \times 10 ^ { 2 }$ 
B)  $4.368 \times 10 ^ { 4 }$ 
C)  $3.048 \times 10 ^ { 36 }$ 
D)  $1.183 \times 10 ^ { 2 }$ 
E)  $2.777 \times 10 ^ { 21 }$

Question 12

Evaluate the function at the indicated value of x.Round your result to three decimal places. 
Function
Value $f ( x ) = 0.7 ^ { x }$ $x = 1.7$

Accepted Answer

A)  $- 0.545$ 
B)  $1.7$ 
C)  $0.55$ 
D)  $0.7$ 
E)  $- 1.7$ 
A)  $- 0.545$ 
B)  $1.7$ 
C)  $0.55$ 
D)  $0.7$ 
E)  $- 1.7$

Question 13

Select the graph of the function.  $f ( x ) = \ln ( x + 9 )$

Accepted Answer

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

Question 14

Use the One-to-One Property to solve the equation for x.  $e ^ { 6 x + 5 } = e ^ { 6 }$

Accepted Answer

A)  $x = - \frac { 1 } { 6 }$ 
B)  $x ^ { 2 } = 6$ 
C)  $x = - 6$ 
D)  $x = \frac { 1 } { 6 }$ 
E)  $x = 6$ 
A)  $x = - \frac { 1 } { 6 }$ 
B)  $x ^ { 2 } = 6$ 
C)  $x = - 6$ 
D)  $x = \frac { 1 } { 6 }$ 
E)  $x = 6$

Question 15

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.  $\log _ { 5 } ( 5 x - 3 ) = \log _ { 5 } ( 4 x + 4 )$

Accepted Answer

A) 8 
B) 6 
C) -1 
D) 7 
E) 9 
A) 8 
B) 6 
C) -1 
D) 7 
E) 9

Question 16

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places.  $x = \frac { 1 } { 100 }$

Accepted Answer

A) -0.5 
B) 0.01 
C) 0.5 
D) -2 
E) 2 
A) -0.5 
B) 0.01 
C) 0.5 
D) -2 
E) 2

Question 17

Rewrite the logarithmic equation $\log _ { 4 } \frac { 1 } { 16 } = - 2$ in exponential form.

Accepted Answer

A)  $4 ^ { 16 } = - 2$ 
B)  $4 ^ { 1 / 16 } = - 2$ 
C)  $4 ^ { - 2 } = \frac { 1 } { 16 }$ 
D)  $\left( \frac { 1 } { 16 } \right) ^ { - 2 } = 4$ 
E)  $4 ^ { - 2 } = - \frac { 1 } { 16 }$ 
A)  $4 ^ { 16 } = - 2$ 
B)  $4 ^ { 1 / 16 } = - 2$ 
C)  $4 ^ { - 2 } = \frac { 1 } { 16 }$ 
D)  $\left( \frac { 1 } { 16 } \right) ^ { - 2 } = 4$ 
E)  $4 ^ { - 2 } = - \frac { 1 } { 16 }$

Question 18

Determine whether or not $x = \frac { 3 } { 7 }$ is a solution to $3 ^ { 3 x - 3 } = 81$ .

Accepted Answer

A) True 
 B)False

Question 19

Evaluate the function at the indicated value of $x = b ^ { - 7 }$ .  $g ( x ) = \log _ { b } x$

Accepted Answer

A) 7 
B) 0 
C)  $\frac { 1 } { 7 }$ 
D) -7 
E)  $- \frac { 1 } { 7 }$ 
A) 7 
B) 0 
C)  $\frac { 1 } { 7 }$ 
D) -7 
E)  $- \frac { 1 } { 7 }$

Question 20

Select the graph of the exponential function.   $f ( x ) = 6 ^ { x - 2 } + 6$

Accepted Answer

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

Write the exponential equation in logarithmic form. $2 ^ { 3 } = 8$

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places. $x = 25.5$

Graph the function using translations. $f ( x ) = e ^ { x + 1 } + 2$

Rewrite the logarithm as a ratio of common logarithms. Log_2.7 x

Condense the expression log₄ x + log₄ 3 to the logarithm of a single term.

Use the properties of logarithms to rewrite and simplify the logarithmic expression. Log₂ (4² · 7⁴⁾

Solve the exponential equation algebraically.Approximate the result to three decimal places. $1000 e ^ { - 4 x } = 75$

Evaluate the function at the indicated value of $x = 281 ^ { 5 }$ . $g ( x ) = \log _ { 281 } x$

Solve for x. $6 ^ { x } = 36$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $- 22 + 4 e ^ { x } = 13$

Evaluate the function at the indicated value of $x$ .Round your result to three decimal places. Function Value $f ( x ) = 200 ( 1.3 ) ^ { 12 x }$ $x = 14$

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value $f ( x ) = 0.7 ^ { x }$ $x = 1.7$

Select the graph of the function. $f ( x ) = \ln ( x + 9 )$

Use the One-to-One Property to solve the equation for x. $e ^ { 6 x + 5 } = e ^ { 6 }$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\log _ { 5 } ( 5 x - 3 ) = \log _ { 5 } ( 4 x + 4 )$

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places. $x = \frac { 1 } { 100 }$

Rewrite the logarithmic equation $\log _ { 4 } \frac { 1 } { 16 } = - 2$ in exponential form.

Determine whether or not $x = \frac { 3 } { 7 }$ is a solution to $3 ^ { 3 x - 3 } = 81$ .

Evaluate the function at the indicated value of $x = b ^ { - 7 }$ . $g ( x ) = \log _ { b } x$

Select the graph of the exponential function. $f ( x ) = 6 ^ { x - 2 } + 6$

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 3: Exponential and Logarithmic Functions

Write the exponential equation in logarithmic form. 23=82 ^ { 3 } = 823=8

Evaluate f(x)=log⁡xf ( x ) = \log xf(x)=logx at the indicated value of x.Round your result to three decimal places. x=25.5x = 25.5x=25.5

Graph the function using translations. f(x)=ex+1+2f ( x ) = e ^ { x + 1 } + 2f(x)=ex+1+2

Rewrite the logarithm as a ratio of common logarithms. Log2.7 x

Condense the expression log4 x + log4 3 to the logarithm of a single term.

Use the properties of logarithms to rewrite and simplify the logarithmic expression. ​ Log2 (42 · 74) ​

Solve the exponential equation algebraically.Approximate the result to three decimal places. 1000e−4x=751000 e ^ { - 4 x } = 751000e−4x=75

Evaluate the function at the indicated value of x=2815x = 281 ^ { 5 }x=2815 . g(x)=log⁡281xg ( x ) = \log _ { 281 } xg(x)=log281​x

Solve for x. 6x=366 ^ { x } = 366x=36

Solve the exponential equation algebraically.Approximate the result to three decimal places. −22+4ex=13- 22 + 4 e ^ { x } = 13−22+4ex=13

Evaluate the function at the indicated value of xxx .Round your result to three decimal places. Function Value f(x)=200(1.3)12xf ( x ) = 200 ( 1.3 ) ^ { 12 x }f(x)=200(1.3)12x x=14x = 14x=14

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value f(x)=0.7xf ( x ) = 0.7 ^ { x }f(x)=0.7x x=1.7x = 1.7x=1.7

Select the graph of the function. f(x)=ln⁡(x+9)f ( x ) = \ln ( x + 9 )f(x)=ln(x+9)

Use the One-to-One Property to solve the equation for x. e6x+5=e6e ^ { 6 x + 5 } = e ^ { 6 }e6x+5=e6

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. log⁡5(5x−3)=log⁡5(4x+4)\log _ { 5 } ( 5 x - 3 ) = \log _ { 5 } ( 4 x + 4 )log5​(5x−3)=log5​(4x+4)

Evaluate f(x)=log⁡xf ( x ) = \log xf(x)=logx at the indicated value of x.Round your result to three decimal places. x=1100x = \frac { 1 } { 100 }x=1001​

Rewrite the logarithmic equation log⁡4116=−2\log _ { 4 } \frac { 1 } { 16 } = - 2log4​161​=−2 in exponential form.

Determine whether or not x=37x = \frac { 3 } { 7 }x=73​ is a solution to 33x−3=813 ^ { 3 x - 3 } = 8133x−3=81 .

Evaluate the function at the indicated value of x=b−7x = b ^ { - 7 }x=b−7 . g(x)=log⁡bxg ( x ) = \log _ { b } xg(x)=logb​x

Select the graph of the exponential function. f(x)=6x−2+6f ( x ) = 6 ^ { x - 2 } + 6f(x)=6x−2+6

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Write the exponential equation in logarithmic form. $2 ^ { 3 } = 8$

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places. $x = 25.5$

Graph the function using translations. $f ( x ) = e ^ { x + 1 } + 2$

Rewrite the logarithm as a ratio of common logarithms. Log_2.7 x

Condense the expression log₄ x + log₄ 3 to the logarithm of a single term.

Use the properties of logarithms to rewrite and simplify the logarithmic expression. Log₂ (4² · 7⁴⁾

Solve the exponential equation algebraically.Approximate the result to three decimal places. $1000 e ^ { - 4 x } = 75$

Evaluate the function at the indicated value of $x = 281 ^ { 5 }$ . $g ( x ) = \log _ { 281 } x$

Solve for x. $6 ^ { x } = 36$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $- 22 + 4 e ^ { x } = 13$

Evaluate the function at the indicated value of $x$ .Round your result to three decimal places. Function Value $f ( x ) = 200 ( 1.3 ) ^ { 12 x }$ $x = 14$

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value $f ( x ) = 0.7 ^ { x }$ $x = 1.7$

Select the graph of the function. $f ( x ) = \ln ( x + 9 )$

Use the One-to-One Property to solve the equation for x. $e ^ { 6 x + 5 } = e ^ { 6 }$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\log _ { 5 } ( 5 x - 3 ) = \log _ { 5 } ( 4 x + 4 )$

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places. $x = \frac { 1 } { 100 }$

Rewrite the logarithmic equation $\log _ { 4 } \frac { 1 } { 16 } = - 2$ in exponential form.

Determine whether or not $x = \frac { 3 } { 7 }$ is a solution to $3 ^ { 3 x - 3 } = 81$ .

Evaluate the function at the indicated value of $x = b ^ { - 7 }$ . $g ( x ) = \log _ { b } x$

Select the graph of the exponential function. $f ( x ) = 6 ^ { x - 2 } + 6$