Question 1

Write as an exponential equation.
-$$\log _ { 17 } \sqrt [ 4 ] { 17 } = \frac { 1 } { 4 }$$

Accepted Answer

A)  $\left( \frac { 1 } { 4 } \right) ^ { 17 } = \sqrt [ 4 ] { 17 }$ 
B)  $( \sqrt [ 4 ] { 17 } ) ^ { 1 / 4 } = 17$ 
C)  $17 ^ { 1 / 4 } = \sqrt [ 4 ] { 17 }$ 
D)  $1 \sqrt { 4 } ^ { 17 } = \frac { 1 } { 4 }$ 
A)  $\left( \frac { 1 } { 4 } \right) ^ { 17 } = \sqrt [ 4 ] { 17 }$ 
B)  $( \sqrt [ 4 ] { 17 } ) ^ { 1 / 4 } = 17$ 
C)  $17 ^ { 1 / 4 } = \sqrt [ 4 ] { 17 }$ 
D)  $1 \sqrt { 4 } ^ { 17 } = \frac { 1 } { 4 }$

Question 2

Solve the equation for x. Give an exact solution.
-$$\ln ( 7 x + 5 ) = - 0.1$$

Accepted Answer

A)  $\left\{ \frac { e ^ { - 0.1 } - 5 } { 7 } \right\}$ 
B)  $\left\{ \frac { e ^ { - 0.1 } + 7 } { 5 } \right\}$ 
C)  $\left\{ e ^ { - 0.1 } - 5 \right\}$ 
D)  $\left\{ 7 \left( e ^ { - 0.1 } - 5 \right) \right\}$ 
A)  $\left\{ \frac { e ^ { - 0.1 } - 5 } { 7 } \right\}$ 
B)  $\left\{ \frac { e ^ { - 0.1 } + 7 } { 5 } \right\}$ 
C)  $\left\{ e ^ { - 0.1 } - 5 \right\}$ 
D)  $\left\{ 7 \left( e ^ { - 0.1 } - 5 \right) \right\}$

Question 3

Graph the exponential function.
-$f(x)=3^{x}+1$

Accepted Answer

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

Question 4

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$6 \log _ { b } m - \log _ { b } n$

Accepted Answer

A)  $\log _ { \mathrm { b } } \mathrm { m } 6 \div \log _ { \mathrm { b } } \mathrm { n }$ 
B)  $\log _ { \mathrm { b } } ( \mathrm { m } 6 - \mathrm { n } )$ 
C)  $\log _ { \mathrm { b } } \frac { \mathrm { m } ^ { 6 } } { \mathrm { n } }$ 
D)  $\log _ { \mathrm { b } } \frac { 6 \mathrm {~m} } { \mathrm { n } }$ 
A)  $\log _ { \mathrm { b } } \mathrm { m } 6 \div \log _ { \mathrm { b } } \mathrm { n }$ 
B)  $\log _ { \mathrm { b } } ( \mathrm { m } 6 - \mathrm { n } )$ 
C)  $\log _ { \mathrm { b } } \frac { \mathrm { m } ^ { 6 } } { \mathrm { n } }$ 
D)  $\log _ { \mathrm { b } } \frac { 6 \mathrm {~m} } { \mathrm { n } }$

Question 5

Provide an appropriate response.
-Solve $10 ^ { x - 5 } = \frac { 1 } { 100 }$ for $x$. Give an exact solution.

Accepted Answer

A)  $\{ 7 \}$ 
B)  $\{ \log 5 \}$ 
C)  $\left\{ \frac { 11 } { 2 } \right\}$ 
D)  $\{ 3 \}$ 
A)  $\{ 7 \}$ 
B)  $\{ \log 5 \}$ 
C)  $\left\{ \frac { 11 } { 2 } \right\}$ 
D)  $\{ 3 \}$

Question 6

Write as an exponential equation.
-$\log _ { 10 } 0.0001 = - 4$

Accepted Answer

A)  $10 ^ { - 4 } = 0.0001$ 
B)  $10 ^ { 4 } = 0.0001$ 
C)  $- 4 ^ { 10 } = 0.0001$ 
D)  $0.0001 ^ { 4 } = 10$ 
A)  $10 ^ { - 4 } = 0.0001$ 
B)  $10 ^ { 4 } = 0.0001$ 
C)  $- 4 ^ { 10 } = 0.0001$ 
D)  $0.0001 ^ { 4 } = 10$

Question 7

For the given one-to-one function f, find the following.
-$$f ( x ) = \sqrt { 6 x - 5 } - 5$$
Find $f ( 5 )$ and $f ^ { - 1 } ( 0 )$.

Accepted Answer

A)  $f ( 5 ) = 25 ; f ^ { - 1 } ( 0 ) = 5$ 
B)  $\mathrm { f } ( 5 ) = \frac { 25 } { 6 } ; \mathrm { f } ^ { - 1 } ( 0 ) = 0$ 
C)  $\mathrm { f } ( 5 ) = 0 ; \mathrm { f } ^ { - 1 } ( 0 ) = 5$ 
D)  $f ( 5 ) = 5 ; f ^ { - 1 } ( 0 ) = 0$ 
A)  $f ( 5 ) = 25 ; f ^ { - 1 } ( 0 ) = 5$ 
B)  $\mathrm { f } ( 5 ) = \frac { 25 } { 6 } ; \mathrm { f } ^ { - 1 } ( 0 ) = 0$ 
C)  $\mathrm { f } ( 5 ) = 0 ; \mathrm { f } ^ { - 1 } ( 0 ) = 5$ 
D)  $f ( 5 ) = 5 ; f ^ { - 1 } ( 0 ) = 0$

Question 8

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$$\log _ { 6 } 9 - \log _ { 6 } x$$

Accepted Answer

A)  $\log _ { 6 } ( 9 - x )$ 
B)  $\log _ { 6 } \frac { x } { 9 }$ 
C)  $\log _ { 6 } \frac { 9 } { x }$ 
D)  $\log _ { 12 } \frac { 9 } { x }$ 
A)  $\log _ { 6 } ( 9 - x )$ 
B)  $\log _ { 6 } \frac { x } { 9 }$ 
C)  $\log _ { 6 } \frac { 9 } { x }$ 
D)  $\log _ { 12 } \frac { 9 } { x }$

Question 9

Solve.
-The amount of a radioactive substance present, in grams, at time t in months is given by the formula y = 7000(3)-0.2t. Find the number of grams present in 3 years. If necessary, round to three decimal places.

Accepted Answer

A)  0.257 
B)  362.097 
C)  3620.973 
D)  2.569 
A)  0.257 
B)  362.097 
C)  3620.973 
D)  2.569

Question 10

Solve the equation. Give an approximate solution to four decimal places.
-$7 ^ { 5 x } = 4.5$

Accepted Answer

A)  $\{ 0.1546 \}$ 
B)  $\{ 0.1335 \}$ 
C)  $\{ 3.7219 \}$ 
D)  $\{ 3.8647 \}$ 
A)  $\{ 0.1546 \}$ 
B)  $\{ 0.1335 \}$ 
C)  $\{ 3.7219 \}$ 
D)  $\{ 3.8647 \}$

Question 11

Solve the equation.
-$\ln 2 + \ln x = 0$

Accepted Answer

A)  $\{ \sqrt { 2 } \}$ 
B)  $\{ 2 \}$ 
C)  $\left\{ \frac { 1 } { 2 } \right\}$ 
D)  $\{ \varnothing \mid$ 
A)  $\{ \sqrt { 2 } \}$ 
B)  $\{ 2 \}$ 
C)  $\left\{ \frac { 1 } { 2 } \right\}$ 
D)  $\{ \varnothing \mid$

Question 12

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
-$\begin{array}{l|c|c|c|c|c}
\text { Weekdays (input) } & \text { Mon. } & \text { Tue. } & \text { Wed. } & \text { Thu. } & \text { Fri. } \
\hline \text { Student: Avg. } & & & & & \
\text { Minutes of Study(outputti380 } & 330 & 186 & 330 & 121
\end{array}$

Accepted Answer

A) $\begin{array}{l|c|c|c|c|c}
\text { Student: Avg. } & & & & & \
\text { Minutes of Study(inputt)380 } & 330 & 186 & 330 & 121 \
\hline \text { Weekdays (output) } & \text { Mon. } & \text { Tue. } & \text { Wed. } & \text { Thu. } & \text { Fri. }
\end{array}$ 
B) $\begin{array}{l}
\text { Student: Avg. }\
\begin{array}{l|c|c|c|c|c}
\text { Student: Avg. } & & & & & \
\text { Minutes of Study(inputt)121 } & 330 & 186 & 330 & 380 \
\hline \text { Weekdays (output) } & \text { Mon. } & \text { Tue. } & \text { Wed. } & \text { Thu. } & \text { Fri. }
\end{array}
\end{array}$ 
C) $\begin{array}{l|l|l|l|l|l}
\text { Weekdays (input) } & \text { Mon. } & \text { Tue. } & \text { Wed. } & \text { Thu. } & \text { Fri. } \
\hline \text { Student: Avg. } & & & & & \
\text { Minutes of Study(outpult)380 } & 330 & 186 & 330 & 121
\end{array}$ 
D) $\text { not one-to-one }$ 
A) $\begin{array}{l|c|c|c|c|c}
\text { Student: Avg. } & & & & & \
\text { Minutes of Study(inputt)380 } & 330 & 186 & 330 & 121 \
\hline \text { Weekdays (output) } & \text { Mon. } & \text { Tue. } & \text { Wed. } & \text { Thu. } & \text { Fri. }
\end{array}$ 
B) $\begin{array}{l}
\text { Student: Avg. }\
\begin{array}{l|c|c|c|c|c}
\text { Student: Avg. } & & & & & \
\text { Minutes of Study(inputt)121 } & 330 & 186 & 330 & 380 \
\hline \text { Weekdays (output) } & \text { Mon. } & \text { Tue. } & \text { Wed. } & \text { Thu. } & \text { Fri. }
\end{array}
\end{array}$ 
C) $\begin{array}{l|l|l|l|l|l}
\text { Weekdays (input) } & \text { Mon. } & \text { Tue. } & \text { Wed. } & \text { Thu. } & \text { Fri. } \
\hline \text { Student: Avg. } & & & & & \
\text { Minutes of Study(outpult)380 } & 330 & 186 & 330 & 121
\end{array}$ 
D) $\text { not one-to-one }$

Question 13

Provide an appropriate response.
-Solve $3 ^ { 2 x + 5 } = 6$ for $x$. Give an exact solution and a four-decimal-place approximation.

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } \left( \frac { \log 6 } { \log 3 } - 5 \right) \right\} ; \{ - 1.6845 \}$ 
B)  $\left\{ \frac { \log 1 } { 2 \log 3 } \right\} ; \{ 0.0000 \}$ 
C)  $\left\{ - \frac { 3 } { 2 } \right\} ; \{ - 1.5000 \}$ 
D)  $\left\{ \frac { 1 } { 2 } \left( \frac { \log 3 } { \log 6 } - 5 \right) \right\} ; \{ - 2.1934 \}$ 
A)  $\left\{ \frac { 1 } { 2 } \left( \frac { \log 6 } { \log 3 } - 5 \right) \right\} ; \{ - 1.6845 \}$ 
B)  $\left\{ \frac { \log 1 } { 2 \log 3 } \right\} ; \{ 0.0000 \}$ 
C)  $\left\{ - \frac { 3 } { 2 } \right\} ; \{ - 1.5000 \}$ 
D)  $\left\{ \frac { 1 } { 2 } \left( \frac { \log 3 } { \log 6 } - 5 \right) \right\} ; \{ - 2.1934 \}$

Question 14

For the given functions f and g, find the composition.
-$$f ( x ) = x ^ { 2 } + 2 x ; g ( x ) = x + 4$$
Find $( f \circ g ) ( 3 )$.

Accepted Answer

A)  $2 \sqrt { 3 }$ 
B)  0 
C)  63 
D)  19 
A)  $2 \sqrt { 3 }$ 
B)  0 
C)  63 
D)  19

Question 15

Use the following approximations to find the approximate value of the logarithmic expression: $\log _ { b } 3 \approx 0.5$ logb $8 \approx 0.9$
$\log _ { b } 5 \approx 0.7$ logb $20 \approx 1.3$
-$\log _ { b } 160$

Accepted Answer

A)  $1.17$ 
B)  28 
C)  160 
D)  $2.2$ 
A)  $1.17$ 
B)  28 
C)  160 
D)  $2.2$

Question 16

Find the value of the logarithmic expression.
-$\log _ { 3 } \frac { 1 } { 27 }$

Accepted Answer

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

Question 17

Determine whether the function is a one-to-one function.
-$$f = \{ ( 6 , - 5 ) , ( - 4 , - 4 ) , ( - 6 , - 3 ) , ( - 8 , - 2 ) \}$$

Accepted Answer

A)  one-to-one 
B)  not one-to-one 
A)  one-to-one 
B)  not one-to-one

Question 18

Graph the exponential function.
-$y=-\left(\frac{1}{5}\right)^{x}$

Accepted Answer

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

Question 19

Solve the logarithmic equation. Give an exact solution.
-$$\log _ { 7 } ( 3 x - 5 ) = 2$$

Accepted Answer

A)  $\{ 18 \}$ 
B)  $\left\{ \frac { 19 } { 3 } \right\}$ 
C)  $\left\{ \frac { 44 } { 3 } \right\}$ 
D)  $\{ 15 \}$ 
A)  $\{ 18 \}$ 
B)  $\left\{ \frac { 19 } { 3 } \right\}$ 
C)  $\left\{ \frac { 44 } { 3 } \right\}$ 
D)  $\{ 15 \}$

Question 20

For the given functions f and g, find the composition.
-$$f ( x ) = - 2 x + 5 ; g ( x ) = 5 x + 9$$
Find $( g \circ f ) ( x )$.

Accepted Answer

A)  $10 x + 34$ 
B)  $- 10 x + 34$ 
C)  $- 10 x + 23$ 
D)  $- 10 x - 16$ 
A)  $10 x + 34$ 
B)  $- 10 x + 34$ 
C)  $- 10 x + 23$ 
D)  $- 10 x - 16$

Write as an exponential equation. - $\log _ { 17 } \sqrt [ 4 ] { 17 } = \frac { 1 } { 4 }$

Solve the equation for x. Give an exact solution. - $\ln ( 7 x + 5 ) = - 0.1$

Graph the exponential function. - $f(x)=3^{x}+1$ $Graph the exponential function. - f(x)=3^{x}+1$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $6 \log _ { b } m - \log _ { b } n$

Provide an appropriate response. -Solve $10 ^ { x - 5 } = \frac { 1 } { 100 }$ for $x$ . Give an exact solution.

Write as an exponential equation. - $\log _ { 10 } 0.0001 = - 4$

For the given one-to-one function f, find the following. - $f ( x ) = \sqrt { 6 x - 5 } - 5$ Find $f ( 5 )$ and $f ^ { - 1 } ( 0 )$ .

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 6 } 9 - \log _ { 6 } x$

Solve. -The amount of a radioactive substance present, in grams, at time t in months is given by the formula y = 7000(3)-0.2t. Find the number of grams present in 3 years. If necessary, round to three decimal places.

Solve the equation. Give an approximate solution to four decimal places. - $7 ^ { 5 x } = 4.5$

Solve the equation. - $\ln 2 + \ln x = 0$

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - Weekdays (input) Mon. Tue. Wed. Thu. Fri. Student: Avg. Minutes of Study(outputti380 330 186 330 121

Provide an appropriate response. -Solve $3 ^ { 2 x + 5 } = 6$ for $x$ . Give an exact solution and a four-decimal-place approximation.

For the given functions f and g, find the composition. - $f ( x ) = x ^ { 2 } + 2 x ; g ( x ) = x + 4$ Find $( f \circ g ) ( 3 )$ .

Use the following approximations to find the approximate value of the logarithmic expression: $\log _ { b } 3 \approx 0.5$ logb $8 \approx 0.9$ $\log _ { b } 5 \approx 0.7$ logb $20 \approx 1.3$ - $\log _ { b } 160$

Find the value of the logarithmic expression. - $\log _ { 3 } \frac { 1 } { 27 }$

Determine whether the function is a one-to-one function. - $f = \{ ( 6 , - 5 ) , ( - 4 , - 4 ) , ( - 6 , - 3 ) , ( - 8 , - 2 ) \}$

Graph the exponential function. - $y=-\left(\frac{1}{5}\right)^{x}$ $Graph the exponential function. - y=-\left(\frac{1}{5}\right)^{x}$

Solve the logarithmic equation. Give an exact solution. - $\log _ { 7 } ( 3 x - 5 ) = 2$

For the given functions f and g, find the composition. - $f ( x ) = - 2 x + 5 ; g ( x ) = 5 x + 9$ Find $( g \circ f ) ( x )$ .

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

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Exam 9: Exponential and Logarithmic Functions

Write as an exponential equation. - log⁡17174=14\log _ { 17 } \sqrt [ 4 ] { 17 } = \frac { 1 } { 4 }log17​417​=41​

Solve the equation for x. Give an exact solution. - ln⁡(7x+5)=−0.1\ln ( 7 x + 5 ) = - 0.1ln(7x+5)=−0.1

Graph the exponential function. - f(x)=3x+1f(x)=3^{x}+1f(x)=3x+1

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - 6log⁡bm−log⁡bn6 \log _ { b } m - \log _ { b } n6logb​m−logb​n

Provide an appropriate response. -Solve 10x−5=110010 ^ { x - 5 } = \frac { 1 } { 100 }10x−5=1001​ for xxx . Give an exact solution.

Write as an exponential equation. - log⁡100.0001=−4\log _ { 10 } 0.0001 = - 4log10​0.0001=−4

For the given one-to-one function f, find the following. - f(x)=6x−5−5f ( x ) = \sqrt { 6 x - 5 } - 5f(x)=6x−5​−5 Find f(5)f ( 5 )f(5) and f−1(0)f ^ { - 1 } ( 0 )f−1(0) .

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡69−log⁡6x\log _ { 6 } 9 - \log _ { 6 } xlog6​9−log6​x