Question 1

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$$\log _ { 4 } \frac { 625 } { 7 }$$

Accepted Answer

A)  $\log _ { 4 } 7 - \log _ { 4 } 625$ 
B)  $\log _ { 4 } 625 + \log _ { 4 } 7$ 
C)  $\log _ { 4 } 625 - \log _ { 4 } 7$ 
D)  $\log _ { 4 } 5 - \log _ { 4 } 7$ 
A)  $\log _ { 4 } 7 - \log _ { 4 } 625$ 
B)  $\log _ { 4 } 625 + \log _ { 4 } 7$ 
C)  $\log _ { 4 } 625 - \log _ { 4 } 7$ 
D)  $\log _ { 4 } 5 - \log _ { 4 } 7$

Question 2

Find the antilog of the logarithm. Round the answer to six decimal places.
-2.6084

Accepted Answer

A) 405.882195 
B) 1.823224 
C) 0.002464 
D) 0.073652 
A) 405.882195 
B) 1.823224 
C) 0.002464 
D) 0.073652

Question 3

Determine whether the function is a one-to-one function.
-$$\{ ( 6 , - 7 ) , ( - 1 , - 6 ) , ( - 3 , - 5 ) , ( - 5 , - 4 ) \}$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 4

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places.
-4698

Accepted Answer

A) 3.6728 
B) 8.4549 
C) 3.6710 
D) 3.6719 
A) 3.6728 
B) 8.4549 
C) 3.6710 
D) 3.6719

Question 5

Determine whether the function is a one-to-one function.
-

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 6

Solve the problem.
-The population of a particular country was 21 million in 1984; in 1989, it was 32 million. The exponential growth function $\mathrm { A } = 21 \mathrm { e } ^ { \mathrm { kt } }$ describes the population of this country t years after describes the population of this country t years after 1984. Use the fact that 5 years
After 1984 the population increased by 11 million. Find k rounded to three decimal places.

Accepted Answer

A) 0.084 
B) 1.302 
C) 0.094 
D) 0.480 
A) 0.084 
B) 1.302 
C) 0.094 
D) 0.480

Question 7

Solve the problem.
-The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential
Growth modelel $\mathrm { A } = 1700 \mathrm { e } ^ { 0.047 t }$ . Wh. Wen will the account be worth $2362?

Accepted Answer

A) 2007 
B) 2008 
C) 2006 
D) 2009 
A) 2007 
B) 2008 
C) 2006 
D) 2009

Question 8

Solve the problem.
-The 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 pH of a solution is given by pH = - log(H+)where H+ represents the concentration of the hydrogen ions in
The solution in moles per liter. Find the pH if the hydrogen ion concentration iss $9 \times 10 ^ { - 4 }$

Accepted Answer

A) 3.05 
B) 3.95 
C) 4.95 
D) 4.05 
A) 3.05 
B) 3.95 
C) 4.95 
D) 4.05

Question 9

For the given function, find the domain and range of both f(x)and ${ f } ^ { - 1 } ( \mathrm { x } ).$
-{(6, -12), (5, -11), (3, -10), (1, -9)}

Accepted Answer

A)  f: domain: $\{ - 12 , - 11 , - 10 , - 9 \}$ 
$~~~~$range: $\{ 6,5,3,1 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ 6,5,3,1 \}$
$~~~~$range: $\{ - 12 , - 11 , - 10 , - 9 \}$ 
B)  f: domain: $\{ 6,5,3,1 \}$
$~~~~$range: $\{ - 12 , - 11 , - 10 , - 9 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ - 12 , - 11 , - 10 , - 9 \}$
$~~~~$range: $\{ 6,5,3,1 \}$ 
C)  f: domain: $\{ - 12 , - 11 , - 10 , - 9 \}$ 
$~~~~$range: $\{ 6,5,3,1 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ - 12 , - 11 , - 10 , - 9 \}$ 
$~~~~$range: $\{ 6,5,3,1 \}$ 
D)  f: domain: $\{ 6,5,3,1 \}$ 
$~~~~$range: $\{ - 12 , - 11 , - 10 , - 9 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ 6,5,3,1 \}$
$~~~~$range: $\{ - 12 , - 11 , - 10 , - 9 \}$ 
A)  f: domain: $\{ - 12 , - 11 , - 10 , - 9 \}$ 
$~~~~$range: $\{ 6,5,3,1 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ 6,5,3,1 \}$
$~~~~$range: $\{ - 12 , - 11 , - 10 , - 9 \}$ 
B)  f: domain: $\{ 6,5,3,1 \}$
$~~~~$range: $\{ - 12 , - 11 , - 10 , - 9 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ - 12 , - 11 , - 10 , - 9 \}$
$~~~~$range: $\{ 6,5,3,1 \}$ 
C)  f: domain: $\{ - 12 , - 11 , - 10 , - 9 \}$ 
$~~~~$range: $\{ 6,5,3,1 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ - 12 , - 11 , - 10 , - 9 \}$ 
$~~~~$range: $\{ 6,5,3,1 \}$ 
D)  f: domain: $\{ 6,5,3,1 \}$ 
$~~~~$range: $\{ - 12 , - 11 , - 10 , - 9 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ 6,5,3,1 \}$
$~~~~$range: $\{ - 12 , - 11 , - 10 , - 9 \}$

Question 10

Solve the problem.
-How many times more intense is an earthquake that measures 7.87 on the Richter scale than the minimum level for comparison? Round answer to the nearest integer.

Accepted Answer

A) 79 
B) 8 
C) 74,131,024 
D) 787 
A) 79 
B) 8 
C) 74,131,024 
D) 787

Question 11

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log 3 x = \log 4 + \log ( x - 1 )$$

Accepted Answer

A) 4 
B)  $- \frac { 4 } { 7 }$ 
C)  $\frac { 3 } { 2 }$ 
D) -4 
A) 4 
B)  $- \frac { 4 } { 7 }$ 
C)  $\frac { 3 } { 2 }$ 
D) -4

Question 12

Determine whether the given functions are inverses of each other.
-$$f ( x ) = \sqrt { x } , x \geq 0 , \quad g ( x ) = \frac { 1 } { \sqrt { x } } , x \geq 0$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 13

Determine whether the function is a one-to-one function.
-$$y = x ^ { 2 } + 6$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 14

Graph the function.
-$f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x + 1 }$

Accepted Answer

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

Question 15

For the given function, find the domain and range of both f(x)and ${ f } ^ { - 1 } ( \mathrm { x } ).$
-

Accepted Answer

A)  $\begin{array} { l } 
\mathrm { f } : \quad \text { domain: } \{ x \mid x \geq - 4 \} \
~~~~\text { range: } \{ \mathrm { y } \mid \mathrm { y } \geq 0 \} \
\mathrm { f } ^ { - 1 } : \text { domain: } \{ x \mid \mathrm { x } \geq - 4 \} \
~~~~\text { range: } \{ \mathrm { y } \mid \mathrm { y } \geq 0 \}
\end{array}$ 
B)  f: domain: $\{ x \mid x \geq - 4 \}$ 
$~~~~$range: $\{ y \mid y \geq 0 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ \mathrm { x } \mid \mathrm { x } \geq 0 \}$
$~~~~$range: $\{ y \mid y \geq - 4 \}$ 
C)  f: domain: $\{ x \mid x \geq 0 \}$ 
$~~~~$range: $\{ y \mid y \geq - 4 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ x \mid \mathrm { x } \geq - 4 \}$ 
$~~~~$range: $\{ y \mid y \geq 0 \}$ 
D)  f: domain: $\{ x \mid x \geq 0 \}$ 
$~~~~$range: $\{ y \mid y \geq - 4 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ \mathrm { x } \mid \mathrm { x } \geq 0 \}$ 
$~~~~$range: $\{ y \mid y \geq - 4 \}$ 
A)  $\begin{array} { l } 
\mathrm { f } : \quad \text { domain: } \{ x \mid x \geq - 4 \} \
~~~~\text { range: } \{ \mathrm { y } \mid \mathrm { y } \geq 0 \} \
\mathrm { f } ^ { - 1 } : \text { domain: } \{ x \mid \mathrm { x } \geq - 4 \} \
~~~~\text { range: } \{ \mathrm { y } \mid \mathrm { y } \geq 0 \}
\end{array}$ 
B)  f: domain: $\{ x \mid x \geq - 4 \}$ 
$~~~~$range: $\{ y \mid y \geq 0 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ \mathrm { x } \mid \mathrm { x } \geq 0 \}$
$~~~~$range: $\{ y \mid y \geq - 4 \}$ 
C)  f: domain: $\{ x \mid x \geq 0 \}$ 
$~~~~$range: $\{ y \mid y \geq - 4 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ x \mid \mathrm { x } \geq - 4 \}$ 
$~~~~$range: $\{ y \mid y \geq 0 \}$ 
D)  f: domain: $\{ x \mid x \geq 0 \}$ 
$~~~~$range: $\{ y \mid y \geq - 4 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ \mathrm { x } \mid \mathrm { x } \geq 0 \}$ 
$~~~~$range: $\{ y \mid y \geq - 4 \}$

Question 16

Determine whether the given functions are inverses of each other.
-$$f ( x ) = \sqrt [ 5 ] { x - 3 } , \quad g ( x ) = x ^ { 5 } + 3$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 17

A one-to-one function f is given. $\text { Find } \mathrm { f } ^ { - 1 } ( \mathrm { x } )$ and graph fwith a solid line and $f ^ { - 1 } ( x )$ with a dotted line on the same axes.
-$f ( x ) = \sqrt { x + 5 } , x \geq - 5$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 5 , x \geq 0$
  
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 5 , \mathrm { x } \geq 0$
  
C)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 5 , x \geq 0$
  
D)  $f ^ { - 1 } ( x ) = - x ^ { 2 } + 5 , x \leq 0$
  
A)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 5 , x \geq 0$
  
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 5 , \mathrm { x } \geq 0$
  
C)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 5 , x \geq 0$
  
D)  $f ^ { - 1 } ( x ) = - x ^ { 2 } + 5 , x \leq 0$

Question 18

Evaluate.
-log9 81

Accepted Answer

A) 81 
B) 4 
C) 9 
D) 2 
A) 81 
B) 4 
C) 9 
D) 2

Question 19

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$$\log _ { 3 } ( 2 \cdot 11 )$$

Accepted Answer

A)  $\log _ { 3 } 2 + \log _ { 3 } 11$ 
B)  $\log _ { 3 } 22$ 
C)  $\log _ { 3 } 2 - \log _ { 3 } 11$ 
D)  $\left( \log _ { 3 } 2 \right) \left( \log _ { 3 } 11 \right)$ 
A)  $\log _ { 3 } 2 + \log _ { 3 } 11$ 
B)  $\log _ { 3 } 22$ 
C)  $\log _ { 3 } 2 - \log _ { 3 } 11$ 
D)  $\left( \log _ { 3 } 2 \right) \left( \log _ { 3 } 11 \right)$

Question 20

Evaluate.
-$$\log _ { 3 } 3 + \log _ { 3 } 1$$

Accepted Answer

A) 1 
B) 3 
C) 4 
D) 2 
A) 1 
B) 3 
C) 4 
D) 2

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 4 } \frac { 625 } { 7 }$

Find the antilog of the logarithm. Round the answer to six decimal places. -2.6084

Determine whether the function is a one-to-one function. - $\{ ( 6 , - 7 ) , ( - 1 , - 6 ) , ( - 3 , - 5 ) , ( - 5 , - 4 ) \}$

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places. -4698

Determine whether the function is a one-to-one function. -

For the given function, find the domain and range of both f(x)and ${ f } ^ { - 1 } ( \mathrm { x } ).$ -{(6, -12), (5, -11), (3, -10), (1, -9)}

Solve the problem. -How many times more intense is an earthquake that measures 7.87 on the Richter scale than the minimum level for comparison? Round answer to the nearest integer.

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log 3 x = \log 4 + \log ( x - 1 )$

Determine whether the given functions are inverses of each other. - $f ( x ) = \sqrt { x } , x \geq 0 , \quad g ( x ) = \frac { 1 } { \sqrt { x } } , x \geq 0$

Determine whether the function is a one-to-one function. - $y = x ^ { 2 } + 6$

Graph the function. - $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x + 1 }$ $Graph the function. - f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x + 1 }$

For the given function, find the domain and range of both f(x)and ${ f } ^ { - 1 } ( \mathrm { x } ).$ - $For the given function, find the domain and range of both f(x)and { f } ^ { - 1 } ( \mathrm { x } ). -$

Determine whether the given functions are inverses of each other. - $f ( x ) = \sqrt [ 5 ] { x - 3 } , \quad g ( x ) = x ^ { 5 } + 3$

Evaluate. -log9 81

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 3 } ( 2 \cdot 11 )$

Evaluate. - $\log _ { 3 } 3 + \log _ { 3 } 1$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Exam 9: Exponential and Logarithmic Functions

Use properties of logarithms to expand the logarithmic expression as much as possible. - log⁡46257\log _ { 4 } \frac { 625 } { 7 }log4​7625​

Find the antilog of the logarithm. Round the answer to six decimal places. -2.6084

Determine whether the function is a one-to-one function. - {(6,−7),(−1,−6),(−3,−5),(−5,−4)}\{ ( 6 , - 7 ) , ( - 1 , - 6 ) , ( - 3 , - 5 ) , ( - 5 , - 4 ) \}{(6,−7),(−1,−6),(−3,−5),(−5,−4)}

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places. -4698

Determine whether the function is a one-to-one function. -

For the given function, find the domain and range of both f(x)and f−1(x).{ f } ^ { - 1 } ( \mathrm { x } ).f−1(x). -{(6, -12), (5, -11), (3, -10), (1, -9)}

Solve the problem. -How many times more intense is an earthquake that measures 7.87 on the Richter scale than the minimum level for comparison? Round answer to the nearest integer.

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - log⁡3x=log⁡4+log⁡(x−1)\log 3 x = \log 4 + \log ( x - 1 )log3x=log4+log(x−1)

Determine whether the given functions are inverses of each other. - f(x)=x,x≥0,g(x)=1x,x≥0f ( x ) = \sqrt { x } , x \geq 0 , \quad g ( x ) = \frac { 1 } { \sqrt { x } } , x \geq 0f(x)=x​,x≥0,g(x)=x​1​,x≥0

Determine whether the function is a one-to-one function. - y=x2+6y = x ^ { 2 } + 6y=x2+6

Graph the function. - f(x)=(14)x+1f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x + 1 }f(x)=(41​)x+1

For the given function, find the domain and range of both f(x)and f−1(x).{ f } ^ { - 1 } ( \mathrm { x } ).f−1(x). -

Determine whether the given functions are inverses of each other. - f(x)=x−35,g(x)=x5+3f ( x ) = \sqrt [ 5 ] { x - 3 } , \quad g ( x ) = x ^ { 5 } + 3f(x)=5x−3​,g(x)=x5+3

A one-to-one function f is given. Find f−1(x)\text { Find } \mathrm { f } ^ { - 1 } ( \mathrm { x } ) Find f−1(x) and graph fwith a solid line and f−1(x)f ^ { - 1 } ( x )f−1(x) with a dotted line on the same axes. - f(x)=x+5,x≥−5f ( x ) = \sqrt { x + 5 } , x \geq - 5f(x)=x+5​,x≥−5

Evaluate. -log9 81

Use properties of logarithms to expand the logarithmic expression as much as possible. - log⁡3(2⋅11)\log _ { 3 } ( 2 \cdot 11 )log3​(2⋅11)

Evaluate. - log⁡33+log⁡31\log _ { 3 } 3 + \log _ { 3 } 1log3​3+log3​1

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 4 } \frac { 625 } { 7 }$

Determine whether the function is a one-to-one function. - $\{ ( 6 , - 7 ) , ( - 1 , - 6 ) , ( - 3 , - 5 ) , ( - 5 , - 4 ) \}$

For the given function, find the domain and range of both f(x)and ${ f } ^ { - 1 } ( \mathrm { x } ).$ -{(6, -12), (5, -11), (3, -10), (1, -9)}

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. - $\log 3 x = \log 4 + \log ( x - 1 )$

Determine whether the given functions are inverses of each other. - $f ( x ) = \sqrt { x } , x \geq 0 , \quad g ( x ) = \frac { 1 } { \sqrt { x } } , x \geq 0$

Determine whether the function is a one-to-one function. - $y = x ^ { 2 } + 6$

Graph the function. - $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x + 1 }$ $Graph the function. - f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x + 1 }$

For the given function, find the domain and range of both f(x)and ${ f } ^ { - 1 } ( \mathrm { x } ).$ - $For the given function, find the domain and range of both f(x)and { f } ^ { - 1 } ( \mathrm { x } ). -$

Determine whether the given functions are inverses of each other. - $f ( x ) = \sqrt [ 5 ] { x - 3 } , \quad g ( x ) = x ^ { 5 } + 3$

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { 3 } ( 2 \cdot 11 )$

Evaluate. - $\log _ { 3 } 3 + \log _ { 3 } 1$