Question 1

Solve the equation.
-$$2 ^ { ( 7 - 3 x ) } = \frac { 1 } { 4 }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\{ 1 \}$ 
C)  $\{ 3 \}$ 
D)  $\{ - 3 \}$ 
A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\{ 1 \}$ 
C)  $\{ 3 \}$ 
D)  $\{ - 3 \}$

Question 2

For the function as defined that is one-to-one, graph f and $\mathrm { f } ^ { - 1 }$ on the same axes.
-$f(x)=x^{3}+2$

Accepted Answer

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

Question 3

Use the definition of inverses to determine whether f and g are inverses.
-$$f ( x ) = \frac { 3 + x } { x } , \quad g ( x ) = \frac { 3 } { x - 1 }$$

Accepted Answer

A) True 
 B)False

Question 4

Solve for the indicated variable.
-$\log _ { c } ( z + s ) = \log _ { c } ( 2 z - 4 )$, for $s$

Accepted Answer

A)  $s = \frac { z } { 4 }$ 
B)  $s = \frac { \log _ { c } z } { 4 }$ 
C)  $s = z - 4$ 
D)  $s = \log _ { c } ( z - 4 )$ 
A)  $s = \frac { z } { 4 }$ 
B)  $s = \frac { \log _ { c } z } { 4 }$ 
C)  $s = z - 4$ 
D)  $s = \log _ { c } ( z - 4 )$

Question 5

Give the answer in exact form.
-$$e ^ { 2 x } - 8 e ^ { x } + 15 = 0$$

Accepted Answer

A)  $\left\{ \mathrm { e } ^ { 5 } , \mathrm { e } ^ { 3 } \right\}$ 
B)  $\left\{ \frac { 5 } { e } , \frac { 3 } { e } \right\}$ 
C)  $\{ \ln 5 , \ln 3 \}$ 
D)  $\{ \ln ( - 5 ) , \ln ( - 3 ) \}$ 
A)  $\left\{ \mathrm { e } ^ { 5 } , \mathrm { e } ^ { 3 } \right\}$ 
B)  $\left\{ \frac { 5 } { e } , \frac { 3 } { e } \right\}$ 
C)  $\{ \ln 5 , \ln 3 \}$ 
D)  $\{ \ln ( - 5 ) , \ln ( - 3 ) \}$

Question 6

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ .
-$3 \log _ { 4 } ( 4 x - 2 ) + 6 \log _ { 4 } ( 2 x + 7 )$

Accepted Answer

A)  $\log _ { 4 } \left( ( 4 x - 2 ) ^ { 3 } + ( 2 x + 7 ) ^ { 6 } \right)$ 
B)  $\log _ { 4 } ( 4 x - 2 ) ^ { 3 } ( 2 x + 7 ) ^ { 6 }$ 
C)  $18 \log _ { 4 } ( 4 x - 2 ) ( 2 x + 7 )$ 
D)  $\log _ { 4 } \frac { ( 4 x - 2 ) ^ { 3 } } { ( 2 x + 7 ) ^ { 6 } }$ 
A)  $\log _ { 4 } \left( ( 4 x - 2 ) ^ { 3 } + ( 2 x + 7 ) ^ { 6 } \right)$ 
B)  $\log _ { 4 } ( 4 x - 2 ) ^ { 3 } ( 2 x + 7 ) ^ { 6 }$ 
C)  $18 \log _ { 4 } ( 4 x - 2 ) ( 2 x + 7 )$ 
D)  $\log _ { 4 } \frac { ( 4 x - 2 ) ^ { 3 } } { ( 2 x + 7 ) ^ { 6 } }$

Question 7

An everyday activity is described. Keeping in mind that an inverse operation "undoes" what an operation does, describe each inverse activity.
-setting a clock forward by one hour

Accepted Answer

A)  setting the clock backward by one hour 
B)  moving your schedule backward by one hour 
C)  setting the clock forward by two hours 
D)  leaving the clock as it is 
A)  setting the clock backward by one hour 
B)  moving your schedule backward by one hour 
C)  setting the clock forward by two hours 
D)  leaving the clock as it is

Question 8

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$4 ^ { ( x + 1 ) } = 9.00$

Accepted Answer

A)  {2.05} 
B)  {0.58} 
C)  {1.58} 
D)  {2.58} 
A)  {2.05} 
B)  {0.58} 
C)  {1.58} 
D)  {2.58}

Question 9

If an earthquake measured $4.3$ on the Richter scale, what was the approximate intensity of the earthquake in terms of IO? Intensity on the Richter scale is $\log _ { 10 } \left( \mathrm { I } / \mathrm { I } _ { 0 } \right)$.

Accepted Answer

A)  $16,000 \mathrm { I } _ { 0 }$ 
B)  $2000 \mathrm { I } 0$ 
C)  $74 \mathrm { I } _ { 0 }$ 
D)  $20,000 \mathrm { I } 0$ 
A)  $16,000 \mathrm { I } _ { 0 }$ 
B)  $2000 \mathrm { I } 0$ 
C)  $74 \mathrm { I } _ { 0 }$ 
D)  $20,000 \mathrm { I } 0$

Question 10

Write in logarithmic form.
-$$2 ^ { - 2 } = \frac { 1 } { 4 }$$

Accepted Answer

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

Question 11

If $f ( x ) = 6 ^ { x }$, find $f \left( \log _ { 6 } 4 \right)$.

Accepted Answer

A)  $\log _ { 4 } x$ 
B)  6 
C)  4 
D)  24 
A)  $\log _ { 4 } x$ 
B)  6 
C)  4 
D)  24

Question 12

Find the value. Give an approximation to four decimal places.
-log 4176

Accepted Answer

A)  3.6197 
B)  3.6208 
C)  3.6218 
D)  8.3371 
A)  3.6197 
B)  3.6208 
C)  3.6218 
D)  8.3371

Question 13

Find the function value. If the result is irrational, round your answer to the nearest thousandth.
-$$f ( x ) = \left( \frac { 5 } { 2 } \right) ^ { x }$$

Accepted Answer

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

Question 14

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
-$\log _ { a } \left( 4 x ^ { 6 } y \right)$

Accepted Answer

A)  $\log _ { a } 4 + 6 \log _ { a } x + \log _ { a } y$ 
B)  $\log _ { a } \left( 4 + x ^ { 6 } + y \right)$ 
C)  $\left( \log _ { a } 4 \right) \left( \log _ { a } x \right) \left( \log _ { a } y \right)$ 
D)  $\log _ { a } 4 + \left( \log _ { a } x \right) ^ { 6 } + \log _ { a } y$ 
A)  $\log _ { a } 4 + 6 \log _ { a } x + \log _ { a } y$ 
B)  $\log _ { a } \left( 4 + x ^ { 6 } + y \right)$ 
C)  $\left( \log _ { a } 4 \right) \left( \log _ { a } x \right) \left( \log _ { a } y \right)$ 
D)  $\log _ { a } 4 + \left( \log _ { a } x \right) ^ { 6 } + \log _ { a } y$

Question 15

Write an equivalent expression in exponential form.
-$$\log \sqrt { 7 } 343 = 6$$

Accepted Answer

A)  $343 ^ { 3 } = 7$ 
B)  $73 = 343$ 
C)  $3 ^ { 7 } = 343$ 
D)  $7343 = 3$ 
A)  $343 ^ { 3 } = 7$ 
B)  $73 = 343$ 
C)  $3 ^ { 7 } = 343$ 
D)  $7343 = 3$

Question 16

The hydrogen potential, $\mathrm { pH }$, of a substance is defined by $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$, where $\left[ \mathrm { H } ^ { + } \right]$is measured in moles per liter. Find the pH of a sample of lake water whose $\left[ \mathrm { H } ^ { + } \right]$is $3.05 \times 10 ^ { - 9 }$ moles per liter. (Round to the nearest tenth.)

Accepted Answer

A)  7.3 
B)  10.1 
C)  8.5 
D)  6.4 
A)  7.3 
B)  10.1 
C)  8.5 
D)  6.4

Question 17

Graph the exponential function using transformations where appropriate.
-

Accepted Answer

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

Question 18

Decide whether the given functions are inverses.
-$$\begin{array} { l } 
f = \{ ( 4,8 ) , ( 8 , - 2 ) , ( - 2 , - 7 ) \} \
g = \{ ( 8,4 ) , ( - 2,8 ) , ( - 7,4 ) \}
\end{array}$$

Accepted Answer

A) True 
 B)False

Question 19

Determine whether or not the function is one-to-one.
-$f ( x ) = 6.04$

Accepted Answer

A) True 
 B)False

Question 20

Determine whether the statement is true or false.
-If f is a one-to-one function and the graph of f lies completely within the second quadrant, then the graph of $\mathrm { f } ^ { - 1 }$ lies completely within the fourth quadrant.

Accepted Answer

A) True 
 B)False

Solve the equation. - $2 ^ { ( 7 - 3 x ) } = \frac { 1 } { 4 }$

For the function as defined that is one-to-one, graph f and $\mathrm { f } ^ { - 1 }$ on the same axes. - $f(x)=x^{3}+2$ $For the function as defined that is one-to-one, graph f and \mathrm { f } ^ { - 1 } on the same axes. - f(x)=x^{3}+2$

Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = \frac { 3 + x } { x } , \quad g ( x ) = \frac { 3 } { x - 1 }$

Solve for the indicated variable. - $\log _ { c } ( z + s ) = \log _ { c } ( 2 z - 4 )$ , for $s$

Give the answer in exact form. - $e ^ { 2 x } - 8 e ^ { x } + 15 = 0$

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ . - $3 \log _ { 4 } ( 4 x - 2 ) + 6 \log _ { 4 } ( 2 x + 7 )$

An everyday activity is described. Keeping in mind that an inverse operation "undoes" what an operation does, describe each inverse activity. -setting a clock forward by one hour

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $4 ^ { ( x + 1 ) } = 9.00$

If an earthquake measured $4.3$ on the Richter scale, what was the approximate intensity of the earthquake in terms of IO? Intensity on the Richter scale is $\log _ { 10 } \left( \mathrm { I } / \mathrm { I } _ { 0 } \right)$ .

Write in logarithmic form. - $2 ^ { - 2 } = \frac { 1 } { 4 }$

If $f ( x ) = 6 ^ { x }$ , find $f \left( \log _ { 6 } 4 \right)$ .

Find the value. Give an approximation to four decimal places. -log 4176

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log _ { a } \left( 4 x ^ { 6 } y \right)$

Write an equivalent expression in exponential form. - $\log \sqrt { 7 } 343 = 6$

Graph the exponential function using transformations where appropriate. -

Decide whether the given functions are inverses. - f=\{(4,8),(8,-2),(-2,-7)\} g=\{(8,4),(-2,8),(-7,4)\}

Determine whether or not the function is one-to-one. - $f ( x ) = 6.04$

Determine whether the statement is true or false. -If f is a one-to-one function and the graph of f lies completely within the second quadrant, then the graph of $\mathrm { f } ^ { - 1 }$ lies completely within the fourth quadrant.

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Solve the equation. - 2(7−3x)=142 ^ { ( 7 - 3 x ) } = \frac { 1 } { 4 }2(7−3x)=41​

For the function as defined that is one-to-one, graph f and f−1\mathrm { f } ^ { - 1 }f−1 on the same axes. - f(x)=x3+2f(x)=x^{3}+2f(x)=x3+2

Use the definition of inverses to determine whether f and g are inverses. - f(x)=3+xx,g(x)=3x−1f ( x ) = \frac { 3 + x } { x } , \quad g ( x ) = \frac { 3 } { x - 1 }f(x)=x3+x​,g(x)=x−13​

Solve for the indicated variable. - log⁡c(z+s)=log⁡c(2z−4)\log _ { c } ( z + s ) = \log _ { c } ( 2 z - 4 )logc​(z+s)=logc​(2z−4) , for sss

Give the answer in exact form. - e2x−8ex+15=0e ^ { 2 x } - 8 e ^ { x } + 15 = 0e2x−8ex+15=0

An everyday activity is described. Keeping in mind that an inverse operation "undoes" what an operation does, describe each inverse activity. -setting a clock forward by one hour

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - 4(x+1)=9.004 ^ { ( x + 1 ) } = 9.004(x+1)=9.00

If an earthquake measured 4.34.34.3 on the Richter scale, what was the approximate intensity of the earthquake in terms of IO? Intensity on the Richter scale is log⁡10(I/I0)\log _ { 10 } \left( \mathrm { I } / \mathrm { I } _ { 0 } \right)log10​(I/I0​) .

Write in logarithmic form. - 2−2=142 ^ { - 2 } = \frac { 1 } { 4 }2−2=41​

If f(x)=6xf ( x ) = 6 ^ { x }f(x)=6x , find f(log⁡64)f \left( \log _ { 6 } 4 \right)f(log6​4) .

Find the value. Give an approximation to four decimal places. -log 4176

Find the function value. If the result is irrational, round your answer to the nearest thousandth. - f(x)=(52)xf ( x ) = \left( \frac { 5 } { 2 } \right) ^ { x }f(x)=(25​)x

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - log⁡a(4x6y)\log _ { a } \left( 4 x ^ { 6 } y \right)loga​(4x6y)

Write an equivalent expression in exponential form. - log⁡7343=6\log \sqrt { 7 } 343 = 6log7​343=6

Graph the exponential function using transformations where appropriate. -

Decide whether the given functions are inverses. - f=\{(4,8),(8,-2),(-2,-7)\} g=\{(8,4),(-2,8),(-7,4)\}

Determine whether or not the function is one-to-one. - f(x)=6.04f ( x ) = 6.04f(x)=6.04

Determine whether the statement is true or false. -If f is a one-to-one function and the graph of f lies completely within the second quadrant, then the graph of f−1\mathrm { f } ^ { - 1 }f−1 lies completely within the fourth quadrant.

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Solve the equation. - $2 ^ { ( 7 - 3 x ) } = \frac { 1 } { 4 }$

For the function as defined that is one-to-one, graph f and $\mathrm { f } ^ { - 1 }$ on the same axes. - $f(x)=x^{3}+2$ $For the function as defined that is one-to-one, graph f and \mathrm { f } ^ { - 1 } on the same axes. - f(x)=x^{3}+2$

Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = \frac { 3 + x } { x } , \quad g ( x ) = \frac { 3 } { x - 1 }$

Solve for the indicated variable. - $\log _ { c } ( z + s ) = \log _ { c } ( 2 z - 4 )$ , for $s$

Give the answer in exact form. - $e ^ { 2 x } - 8 e ^ { x } + 15 = 0$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $4 ^ { ( x + 1 ) } = 9.00$

If an earthquake measured $4.3$ on the Richter scale, what was the approximate intensity of the earthquake in terms of IO? Intensity on the Richter scale is $\log _ { 10 } \left( \mathrm { I } / \mathrm { I } _ { 0 } \right)$ .

Write in logarithmic form. - $2 ^ { - 2 } = \frac { 1 } { 4 }$

If $f ( x ) = 6 ^ { x }$ , find $f \left( \log _ { 6 } 4 \right)$ .

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log _ { a } \left( 4 x ^ { 6 } y \right)$

Write an equivalent expression in exponential form. - $\log \sqrt { 7 } 343 = 6$

Determine whether or not the function is one-to-one. - $f ( x ) = 6.04$

Determine whether the statement is true or false. -If f is a one-to-one function and the graph of f lies completely within the second quadrant, then the graph of $\mathrm { f } ^ { - 1 }$ lies completely within the fourth quadrant.