Question 1

Rewrite the logarithm as a ratio of common logarithms. 
$\log _ { 5 } 19$

Accepted Answer

A)  $\frac { \log 19 } { \log 5 }$ 
B)  $\log \frac { 19 } { 5 }$ 
C)  $\frac { \log 5 } { \log 19 }$ 
D)  $\log \frac { 5 } { 19 }$ 
E)  None of these 
A)  $\frac { \log 19 } { \log 5 }$ 
B)  $\log \frac { 19 } { 5 }$ 
C)  $\frac { \log 5 } { \log 19 }$ 
D)  $\log \frac { 5 } { 19 }$ 
E)  None of these

Question 2

Find the exponential model that $y = a e ^ { b x }$ fits the points shown in the table. $$\begin{array} { | l | l | l | } 
\hline x & 0 & 4 \
\hline y & 25 & 5 \
\hline
\end{array}$$

Accepted Answer

A)  $y = 25 e ^ { - 0.4024 x }$ 
B)  $y = 25 e ^ { 0.5024 x }$ 
C)  $y = - \frac { 1 } { 25 } e ^ { 0.4024 x }$ 
D)  $y = \frac { 1 } { 25 } e ^ { - 0.6024 x }$ 
E)  $y = - \frac { 1 } { 25 } e ^ { - 0.4024 x }$ 
A)  $y = 25 e ^ { - 0.4024 x }$ 
B)  $y = 25 e ^ { 0.5024 x }$ 
C)  $y = - \frac { 1 } { 25 } e ^ { 0.4024 x }$ 
D)  $y = \frac { 1 } { 25 } e ^ { - 0.6024 x }$ 
E)  $y = - \frac { 1 } { 25 } e ^ { - 0.4024 x }$

Question 3

Select the graph of the exponential function. 
$s ( t ) = 2 e ^ { 0.13 t }$

Accepted Answer

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

Question 4

Write the logarithmic equation in exponential form. $$\log _ { 8 } 64 = 2$$

Accepted Answer

A)  $64 ^ { 8 } = 2$ 
B)  $8 ^ { 2 } = 16$ 
C)  $8 ^ { 2 } = 88$ 
D)  $8 ^ { 2 } = 64$ 
E)  $8 ^ { 64 } = 2$ 
A)  $64 ^ { 8 } = 2$ 
B)  $8 ^ { 2 } = 16$ 
C)  $8 ^ { 2 } = 88$ 
D)  $8 ^ { 2 } = 64$ 
E)  $8 ^ { 64 } = 2$

Question 5

Find the magnitude R of each earthquake of intensity I let I0 $=1$. 
I=262300000

Accepted Answer

A)  7.42 
B)  6.42 
C)  8.42 
D)  10.42 
E)  9.42 
A)  7.42 
B)  6.42 
C)  8.42 
D)  10.42 
E)  9.42

Question 6

Select the graph of the exponential function. $$s ( t ) = 5 e ^ { 0.15 t }$$

Accepted Answer

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

Question 7

Evaluate the function at the indicated value of $X$ . Round your result to three decimal places. 
$\begin{array}{ll}\text { Function } & \text { Value } \ f(x)=0.5^{x} & x=1.7\end{array} $

Accepted Answer

A)  $- 0.308$ 
B)  $1.7$ 
C)  $0.308$ 
D)  $0.5$ 
E)  $- 1.7$ 
A)  $- 0.308$ 
B)  $1.7$ 
C)  $0.308$ 
D)  $0.5$ 
E)  $- 1.7$

Question 8

Find the exact value of the logarithmic expression without using a calculator. $$\log _ { 9 } \sqrt [ 5 ] { 9 }$$

Accepted Answer

A)  5 
B)  45 
C)  9 
D)  $\frac { 1 } { 5 }$ 
E)  None of these 
A)  5 
B)  45 
C)  9 
D)  $\frac { 1 } { 5 }$ 
E)  None of these

Question 9

Use the One-to-One Property to solve the equation for x. 
$\log _ { 2 } ( 8 x + 2 ) = \log _ { 2 } 14$

Accepted Answer

A)  8 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 3 } { 2 }$ 
D)  $\frac { 1 } { 14 }$ 
E)  $\frac { 1 } { 8 }$ 
A)  8 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 3 } { 2 }$ 
D)  $\frac { 1 } { 14 }$ 
E)  $\frac { 1 } { 8 }$

Question 10

Use the One-to-One Property to solve the equation for x. $$\log _ { 5 } ( 3 x + 3 ) = \log _ { 5 } 10$$

Accepted Answer

A)  $\frac { 1 } { 10 }$ 
B)  $\frac { 2 } { 13 }$ 
C)  $\frac { 2 } { 7 }$ 
D)  $\frac { 7 } { 3 }$ 
E)  $\frac { 13 } { 2 }$ 
A)  $\frac { 1 } { 10 }$ 
B)  $\frac { 2 } { 13 }$ 
C)  $\frac { 2 } { 7 }$ 
D)  $\frac { 7 } { 3 }$ 
E)  $\frac { 13 } { 2 }$

Question 11

Evaluate the function at the indicated value of $x = a ^ { 2 }$ 
$g ( x ) = \log _ { a } x$

Accepted Answer

A)  $- 2$ 
B)  $\frac { 1 } { 2 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  2 
E)  0 
A)  $- 2$ 
B)  $\frac { 1 } { 2 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  2 
E)  0

Question 12

Find the exact value of the logarithmic expression without using a calculator. 
$\log _ { 9 } \sqrt [ 3 ] { 9 }$

Accepted Answer

A)  3 
B)  $\frac { 1 } { 3 }$ 
C)  9 
D)  27 
E)  None of these 
A)  3 
B)  $\frac { 1 } { 3 }$ 
C)  9 
D)  27 
E)  None of these

Question 13

Solve the exponential equation algebraically. Approximate the result to three deci- mal places. $$e ^ { x } - 7 = 16$$

Accepted Answer

A)  $\ln 23 \approx 3.135$ 
B)  $\ln 23 \approx - 3.135$ 
C)  $\ln 23 \approx - 2.773$ 
D)  $\ln 23 \approx 2.773$ 
E)  $\ln 23 \approx 1.946$ 
A)  $\ln 23 \approx 3.135$ 
B)  $\ln 23 \approx - 3.135$ 
C)  $\ln 23 \approx - 2.773$ 
D)  $\ln 23 \approx 2.773$ 
E)  $\ln 23 \approx 1.946$

Question 14

Evaluate the function at the indicated value of $X$ . Round your result to three deci- mal places. $$\begin{array} { l c } 
\text { Function } & \text { Value } \
f ( x ) = 0.6 ^ { x } & x = 1.1
\end{array}$$

Accepted Answer

A)  $0.57$ 
B)  $- 1.1$ 
C)  $1.1$ 
D)  $0.6$ 
E)  $- 0.57$ 
A)  $0.57$ 
B)  $- 1.1$ 
C)  $1.1$ 
D)  $0.6$ 
E)  $- 0.57$

Question 15

Solve the exponential equation algebraically. Approximate the result to three deci- mal places. $e ^ { x } - 8 = 12$

Accepted Answer

A)  $\ln 20 \approx 2.485$ 
B)  $\ln 20 \approx 2.996$ 
C)  $\ln 20 \approx - 2.485$ 
D)  $\ln 20 \approx 2.079$ 
E)  $\ln 20 \approx - 2.996$ 
A)  $\ln 20 \approx 2.485$ 
B)  $\ln 20 \approx 2.996$ 
C)  $\ln 20 \approx - 2.485$ 
D)  $\ln 20 \approx 2.079$ 
E)  $\ln 20 \approx - 2.996$

Question 16

Write the exponential equation in logarithmic form. $e ^ { 4 x } = 5$

Accepted Answer

A)  $\ln 5 = - 4 x$ 
B) $\ln 5 = - \frac { 1 } { 4 } x$ 
C) $\ln 5 = \frac { 1 } { 4 } x$ 
D)  $\ln 5 = 4 x$ 
E)  $\ln 4 = 5 x$ 
A)  $\ln 5 = - 4 x$ 
B) $\ln 5 = - \frac { 1 } { 4 } x$ 
C) $\ln 5 = \frac { 1 } { 4 } x$ 
D)  $\ln 5 = 4 x$ 
E)  $\ln 4 = 5 x$

Question 17

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$2 \log _ { 2 } ( 0.5 x ) = 23$$

Accepted Answer

A)  $2 \left( 2 ^ { 23 / 2 } \right) \approx 5,792.619$ 
B)  $2 \left( 2 ^ { 23 / 2 } \right) \approx 5,794.619$ 
C)  $2 \left( 2 ^ { 23 / 2 } \right) \approx 5,790.619$ 
D)  $2 \left( 2 ^ { 23 / 2 } \right) \approx 5,791.619$ 
E)  $2 \left( 2 ^ { 23 / 2 } \right) \approx 5,793.619$ 
A)  $2 \left( 2 ^ { 23 / 2 } \right) \approx 5,792.619$ 
B)  $2 \left( 2 ^ { 23 / 2 } \right) \approx 5,794.619$ 
C)  $2 \left( 2 ^ { 23 / 2 } \right) \approx 5,790.619$ 
D)  $2 \left( 2 ^ { 23 / 2 } \right) \approx 5,791.619$ 
E)  $2 \left( 2 ^ { 23 / 2 } \right) \approx 5,793.619$

Question 18

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. 
$$6 \log _ { 3 } ( 0.5 x ) = 5$$

Accepted Answer

A)  $2 \left( 3 ^ { 5 / 6 } \right) \approx 3.996$ 
B)  $2 \left( 3 ^ { 5 / 6 } \right) \approx 6.996$ 
C)  $2 \left( 3 ^ { 5 / 6 } \right) \approx 4.996$ 
D)  $2 \left( 3 ^ { 5 / 6 } \right) \approx 5.996$ 
E)  $2 \left( 3 ^ { 5 / 6 } \right) \approx 2.996$ 
A)  $2 \left( 3 ^ { 5 / 6 } \right) \approx 3.996$ 
B)  $2 \left( 3 ^ { 5 / 6 } \right) \approx 6.996$ 
C)  $2 \left( 3 ^ { 5 / 6 } \right) \approx 4.996$ 
D)  $2 \left( 3 ^ { 5 / 6 } \right) \approx 5.996$ 
E)  $2 \left( 3 ^ { 5 / 6 } \right) \approx 2.996$

Question 19

Write the logarithmic equation in exponential form. $$\log _ { 5 } 25 = 2$$

Accepted Answer

A)  $5 ^ { 25 } = 2$ 
B)  $5 ^ { 2 } = 25$ 
C)  $5 ^ { 2 } = 10$ 
D)  $25 ^ { 5 } = 2$ 
E)  $5 ^ { 2 } = 55$ 
A)  $5 ^ { 25 } = 2$ 
B)  $5 ^ { 2 } = 25$ 
C)  $5 ^ { 2 } = 10$ 
D)  $25 ^ { 5 } = 2$ 
E)  $5 ^ { 2 } = 55$

Question 20

Solve for $X$ . Approximate the result to three decimal places. $\log _ { 3 } x = \frac { 1 } { 2 }$

Accepted Answer

A)  $\sqrt { 3 } \approx - 1.732$ 
B)  $\frac { \sqrt { 3 } } { 3 } \approx 1.732$ 
C)  $\sqrt { 3 } \approx 2$ 
D)  $\sqrt { 3 } \approx 1.732$ 
E)  $\sqrt { 3 } = 1.732$ 
A)  $\sqrt { 3 } \approx - 1.732$ 
B)  $\frac { \sqrt { 3 } } { 3 } \approx 1.732$ 
C)  $\sqrt { 3 } \approx 2$ 
D)  $\sqrt { 3 } \approx 1.732$ 
E)  $\sqrt { 3 } = 1.732$

Rewrite the logarithm as a ratio of common logarithms. $\log _ { 5 } 19$

Find the exponential model that $y = a e ^ { b x }$ fits the points shown in the table. x 0 4 y 25 5

Select the graph of the exponential function. $s ( t ) = 2 e ^ { 0.13 t }$

Write the logarithmic equation in exponential form. $\log _ { 8 } 64 = 2$

Find the magnitude R of each earthquake of intensity I let I₀ $=1$ . I=262300000

Select the graph of the exponential function. $s ( t ) = 5 e ^ { 0.15 t }$

Evaluate the function at the indicated value of $X$ . Round your result to three decimal places. Function Value f(x)=0. x=1.7

Find the exact value of the logarithmic expression without using a calculator. $\log _ { 9 } \sqrt [ 5 ] { 9 }$

Use the One-to-One Property to solve the equation for x. $\log _ { 2 } ( 8 x + 2 ) = \log _ { 2 } 14$

Use the One-to-One Property to solve the equation for x. $\log _ { 5 } ( 3 x + 3 ) = \log _ { 5 } 10$

Evaluate the function at the indicated value of $x = a ^ { 2 }$ $g ( x ) = \log _ { a } x$

Find the exact value of the logarithmic expression without using a calculator. $\log _ { 9 } \sqrt [ 3 ] { 9 }$

Solve the exponential equation algebraically. Approximate the result to three deci- mal places. $e ^ { x } - 7 = 16$

Evaluate the function at the indicated value of $X$ . Round your result to three deci- mal places. Function Value f(x)=0. x=1.1

Solve the exponential equation algebraically. Approximate the result to three deci- mal places. $e ^ { x } - 8 = 12$

Write the exponential equation in logarithmic form. $e ^ { 4 x } = 5$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $2 \log _ { 2 } ( 0.5 x ) = 23$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $6 \log _ { 3 } ( 0.5 x ) = 5$

Write the logarithmic equation in exponential form. $\log _ { 5 } 25 = 2$

Solve for $X$ . Approximate the result to three decimal places. $\log _ { 3 } x = \frac { 1 } { 2 }$

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometry

Analytic Trigonometry

Topics in Analytic Geometry

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Exam 3: Exponential and Logarithmic Functions

Rewrite the logarithm as a ratio of common logarithms. log⁡519\log _ { 5 } 19log5​19

Find the exponential model that y=aebxy = a e ^ { b x }y=aebx fits the points shown in the table. x 0 4 y 25 5

Select the graph of the exponential function. s(t)=2e0.13ts ( t ) = 2 e ^ { 0.13 t }s(t)=2e0.13t

Write the logarithmic equation in exponential form. log⁡864=2\log _ { 8 } 64 = 2log8​64=2

Find the magnitude R of each earthquake of intensity I let I0 =1=1=1 . I=262300000

Select the graph of the exponential function. s(t)=5e0.15ts ( t ) = 5 e ^ { 0.15 t }s(t)=5e0.15t

Evaluate the function at the indicated value of XXX . Round your result to three decimal places. Function Value f(x)=0. x=1.7

Find the exact value of the logarithmic expression without using a calculator. log⁡995\log _ { 9 } \sqrt [ 5 ] { 9 }log9​59​

Use the One-to-One Property to solve the equation for x. log⁡2(8x+2)=log⁡214\log _ { 2 } ( 8 x + 2 ) = \log _ { 2 } 14log2​(8x+2)=log2​14

Use the One-to-One Property to solve the equation for x. log⁡5(3x+3)=log⁡510\log _ { 5 } ( 3 x + 3 ) = \log _ { 5 } 10log5​(3x+3)=log5​10

Evaluate the function at the indicated value of x=a2x = a ^ { 2 }x=a2 g(x)=log⁡axg ( x ) = \log _ { a } xg(x)=loga​x

Find the exact value of the logarithmic expression without using a calculator. log⁡993\log _ { 9 } \sqrt [ 3 ] { 9 }log9​39​

Solve the exponential equation algebraically. Approximate the result to three deci- mal places. ex−7=16e ^ { x } - 7 = 16ex−7=16

Evaluate the function at the indicated value of XXX . Round your result to three deci- mal places. Function Value f(x)=0. x=1.1

Solve the exponential equation algebraically. Approximate the result to three deci- mal places. ex−8=12e ^ { x } - 8 = 12ex−8=12

Write the exponential equation in logarithmic form. e4x=5e ^ { 4 x } = 5e4x=5

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. 2log⁡2(0.5x)=232 \log _ { 2 } ( 0.5 x ) = 232log2​(0.5x)=23

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. 6log⁡3(0.5x)=56 \log _ { 3 } ( 0.5 x ) = 56log3​(0.5x)=5

Write the logarithmic equation in exponential form. log⁡525=2\log _ { 5 } 25 = 2log5​25=2

Solve for XXX . Approximate the result to three decimal places. log⁡3x=12\log _ { 3 } x = \frac { 1 } { 2 }log3​x=21​

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometry

Analytic Trigonometry

Topics in Analytic Geometry

Filters

Rewrite the logarithm as a ratio of common logarithms. $\log _ { 5 } 19$

Find the exponential model that $y = a e ^ { b x }$ fits the points shown in the table. x 0 4 y 25 5

Select the graph of the exponential function. $s ( t ) = 2 e ^ { 0.13 t }$

Write the logarithmic equation in exponential form. $\log _ { 8 } 64 = 2$

Find the magnitude R of each earthquake of intensity I let I₀ $=1$ . I=262300000

Select the graph of the exponential function. $s ( t ) = 5 e ^ { 0.15 t }$

Evaluate the function at the indicated value of $X$ . Round your result to three decimal places. Function Value f(x)=0. x=1.7

Find the exact value of the logarithmic expression without using a calculator. $\log _ { 9 } \sqrt [ 5 ] { 9 }$

Use the One-to-One Property to solve the equation for x. $\log _ { 2 } ( 8 x + 2 ) = \log _ { 2 } 14$

Use the One-to-One Property to solve the equation for x. $\log _ { 5 } ( 3 x + 3 ) = \log _ { 5 } 10$

Evaluate the function at the indicated value of $x = a ^ { 2 }$ $g ( x ) = \log _ { a } x$

Find the exact value of the logarithmic expression without using a calculator. $\log _ { 9 } \sqrt [ 3 ] { 9 }$

Solve the exponential equation algebraically. Approximate the result to three deci- mal places. $e ^ { x } - 7 = 16$

Evaluate the function at the indicated value of $X$ . Round your result to three deci- mal places. Function Value f(x)=0. x=1.1

Solve the exponential equation algebraically. Approximate the result to three deci- mal places. $e ^ { x } - 8 = 12$

Write the exponential equation in logarithmic form. $e ^ { 4 x } = 5$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $2 \log _ { 2 } ( 0.5 x ) = 23$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $6 \log _ { 3 } ( 0.5 x ) = 5$

Write the logarithmic equation in exponential form. $\log _ { 5 } 25 = 2$

Solve for $X$ . Approximate the result to three decimal places. $\log _ { 3 } x = \frac { 1 } { 2 }$