Question 1

Write an equivalent expression in exponential form.
-$\log _ { 1 / 2 } ( x + 4 ) = - 5$

Accepted Answer

A)  32 
B)  40 
C)  36 
D)  28 
A)  32 
B)  40 
C)  36 
D)  28

Question 2

Use properties of logarithms to evaluate the expression.
-If $f ( x ) = \log _ { 6 } x$, find $f \left( 6 ^ { 6 \log _ { 6 } 6 } \right)$

Accepted Answer

A)  36 
B)  1 
C)  6 
D)  0 
A)  36 
B)  1 
C)  6 
D)  0

Question 3

Determine whether the statement is true or false.
-The function f $f ( x ) = m x + b$ b is a one-to-one function for all values of m and b.

Accepted Answer

A) True 
 B)False

Question 4

Match the function with its graph.
-$$f ( x ) = \log _ { 3 } 3 x$$

Accepted Answer

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

Question 5

Solve the equation.
-$$\left( \frac { 8 } { 7 } \right) ^ { x } = \frac { 49 } { 64 }$$

Accepted Answer

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

Question 6

Graph the function.
-$f(x)=\left(\frac{1}{2}\right)^{x}$

Accepted Answer

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

Question 7

Solve the problem.
-An earthquake was recorded with an intensity which was 50,119 times more powerful than a reference level earthquake, or 50,119 · I0. What is the magnitude of this earthquake on the Richter
Scale (rounded to the nearest tenth)? Intensity on the Richter scale is $$\log _ { 10 } \left( \mathrm { I } / \mathrm { I } _ { 0 } \right)$$

Accepted Answer

A)  4.7 
B)  3.7 
C)  10.8 
D)  0.5 
A)  4.7 
B)  3.7 
C)  10.8 
D)  0.5

Question 8

Solve the problem.
-Given that $f ( x ) = e ^ { x - 1 } + 3$, find $f ^ { - 1 } ( x )$ and give the domain and range of $f ^ { - 1 } ( x )$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( \mathrm { x } - 3 ) + 1$, domain $= ( 0 , \infty )$, range $= ( 0 , \infty )$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( x - 1 ) + 3$, domain $= ( - \infty , \infty )$, range $= ( - \infty , \infty )$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( \mathrm { x } - 1 ) + 3$, domain $= ( 3 , \infty )$, range $= ( - \infty , \infty )$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( x - 3 ) + 1$, domain $= ( 3 , \infty )$, range $= ( - \infty , \infty )$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( \mathrm { x } - 3 ) + 1$, domain $= ( 0 , \infty )$, range $= ( 0 , \infty )$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( x - 1 ) + 3$, domain $= ( - \infty , \infty )$, range $= ( - \infty , \infty )$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( \mathrm { x } - 1 ) + 3$, domain $= ( 3 , \infty )$, range $= ( - \infty , \infty )$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( x - 3 ) + 1$, domain $= ( 3 , \infty )$, range $= ( - \infty , \infty )$

Question 9

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent
positive real numbers.
-$$\log _ { 19 } \left( \frac { 10 \sqrt { m } } { n } \right)$$

Accepted Answer

A)  $\log _ { 19 } 10 + \frac { 1 } { 2 } \log _ { 19 } m - \log _ { 19 } n$ 
B)  $\log _ { 19 } n - \log _ { 19 } 10 - \frac { 1 } { 2 } \log _ { 19 } m$ 
C)  $\log _ { 19 } 10 + \sqrt { \log _ { 19 } m } - \log _ { 19 } n$ 
D)  $\log _ { 19 } 10 \cdot \left( \frac { 1 } { 2 } \log _ { 19 } m \right) \div \log _ { 19 } n$ 
A)  $\log _ { 19 } 10 + \frac { 1 } { 2 } \log _ { 19 } m - \log _ { 19 } n$ 
B)  $\log _ { 19 } n - \log _ { 19 } 10 - \frac { 1 } { 2 } \log _ { 19 } m$ 
C)  $\log _ { 19 } 10 + \sqrt { \log _ { 19 } m } - \log _ { 19 } n$ 
D)  $\log _ { 19 } 10 \cdot \left( \frac { 1 } { 2 } \log _ { 19 } m \right) \div \log _ { 19 } n$

Question 10

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$$\mathrm { e } ^ { \mathrm { x } } + \ln \mathrm { x } = 7$$

Accepted Answer

A)  $\{ 3.621 \}$ 
B)  $\{ 1.854 \}$ 
C)  $\{ 1.259 \}$ 
D)  $\{ 2.854 \}$ 
A)  $\{ 3.621 \}$ 
B)  $\{ 1.854 \}$ 
C)  $\{ 1.259 \}$ 
D)  $\{ 2.854 \}$

Question 11

Write an equivalent expression in exponential form.
-$$\log _ { 4 } 1024 = 5$$

Accepted Answer

A)  $4 ^ { 1024 } = 5$ 
B)  $5 ^ { 4 } = 1024$ 
C)  $10245 = 4$ 
D)  $4 ^ { 5 } = 1024$ 
A)  $4 ^ { 1024 } = 5$ 
B)  $5 ^ { 4 } = 1024$ 
C)  $10245 = 4$ 
D)  $4 ^ { 5 } = 1024$

Question 12

Write an equation for the graph given. The graph represents an exponential function f with base 2 or 3, translated and/or
reflected.
-

Accepted Answer

A)  $2 ^ { x + 1 } - 4$ 
B)  $2 ^ { x - 1 } + 4$ 
C)  $2 ^ { x - 1 } - 4$ 
D)  $2 ^ { x + 1 } + 4$ 
A)  $2 ^ { x + 1 } - 4$ 
B)  $2 ^ { x - 1 } + 4$ 
C)  $2 ^ { x - 1 } - 4$ 
D)  $2 ^ { x + 1 } + 4$

Question 13

Write the word or phrase that best completes each statement or answers the question.
-Explain how the graph of $$y = \log _ { 2 } ( x + 4 )$$ an be obtained from the graph of y $$y = \log _ { 2 } x$$

Accepted Answer

The graph

Question 14

Provide an appropriate response.
-Give an equation of the form $f ( x ) = a ^ { x }$ to define the exponential function whose graph contains the point $( 2,16 )$. Assume that $a > 0$.

Accepted Answer

A)  $f ( x ) = 16 ^ { x }$ 
B)  $f ( x ) = 8 ^ { x }$ 
C)  $f ( x ) = 4 ^ { x }$ 
D)  $f ( x ) = 256 ^ { x }$ 
A)  $f ( x ) = 16 ^ { x }$ 
B)  $f ( x ) = 8 ^ { x }$ 
C)  $f ( x ) = 4 ^ { x }$ 
D)  $f ( x ) = 256 ^ { x }$

Question 15

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$\log ( x + 3 ) + 2 = x ^ { 2 } - 2 x + 1$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ - 0.5071,2.6322 \}$ 
C)  $\{ - 0.546,2.659 \}$ 
D)  $\{ - 0.5894,2.646 \}$ 
A)  $\varnothing$ 
B)  $\{ - 0.5071,2.6322 \}$ 
C)  $\{ - 0.546,2.659 \}$ 
D)  $\{ - 0.5894,2.646 \}$

Question 16

The graph of a function f is given. Use the graph to find the indicated value.
-Let f(x) compute the time in hours to travel x miles at 60 miles per hour. What is the interpretation of $\mathrm { f } ^ { - 1 } ( 8 )$

Accepted Answer

A)  The miles traveled in 8 hours at 60 miles per hour 
B)  The miles traveled in 60 hours 
C)  The hours taken to travel 8 miles at 60 miles per hour 
D)  The hours taken to travel 60 miles 
A)  The miles traveled in 8 hours at 60 miles per hour 
B)  The miles traveled in 60 hours 
C)  The hours taken to travel 8 miles at 60 miles per hour 
D)  The hours taken to travel 60 miles

Question 17

Solve the equation and express the solution in exact form.
-$$\log _ { 2 } \sqrt { 2 x ^ { 2 } } = \frac { 5 } { 2 }$$

Accepted Answer

A)  $\{ - 4,4 \}$ 
B)  $\{ 4 \}$ 
C)  $\{ - 2,2 \}$ 
D)  $\{ - 16,16 \}$ 
A)  $\{ - 4,4 \}$ 
B)  $\{ 4 \}$ 
C)  $\{ - 2,2 \}$ 
D)  $\{ - 16,16 \}$

Question 18

Evaluate the logarithm.
-$\log _ { 13 } ( - 1 )$

Accepted Answer

A)  Undefined 
B)  0 
C)  $- 1$ 
D)  1 
A)  Undefined 
B)  0 
C)  $- 1$ 
D)  1

Question 19

Solve the equation and express the solution in exact form.
-$$\ln ( 45 x - 5 ) = \ln 10$$

Accepted Answer

A)  $\left\{ \frac { 14 } { 45 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 3 } \right\}$ 
C)  $\left\{ \frac { 1 } { 9 } \right\}$ 
D)  $\left\{ \frac { 1 } { 3 } \right\}$ 
A)  $\left\{ \frac { 14 } { 45 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 3 } \right\}$ 
C)  $\left\{ \frac { 1 } { 9 } \right\}$ 
D)  $\left\{ \frac { 1 } { 3 } \right\}$

Question 20

Determine whether or not the function is one-to-one.
-$$f ( x ) = 7 x ^ { 3 } + 7$$

Accepted Answer

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

Write an equivalent expression in exponential form. - $\log _ { 1 / 2 } ( x + 4 ) = - 5$

Use properties of logarithms to evaluate the expression. -If $f ( x ) = \log _ { 6 } x$ , find $f \left( 6 ^ { 6 \log _ { 6 } 6 } \right)$

Determine whether the statement is true or false. -The function f $f ( x ) = m x + b$ b is a one-to-one function for all values of m and b.

Match the function with its graph. - $f ( x ) = \log _ { 3 } 3 x$

Solve the equation. - $\left( \frac { 8 } { 7 } \right) ^ { x } = \frac { 49 } { 64 }$

Graph the function. - $f(x)=\left(\frac{1}{2}\right)^{x}$ $Graph the function. - f(x)=\left(\frac{1}{2}\right)^{x}$

Solve the problem. -Given that $f ( x ) = e ^ { x - 1 } + 3$ , find $f ^ { - 1 } ( x )$ and give the domain and range of $f ^ { - 1 } ( x )$

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log _ { 19 } \left( \frac { 10 \sqrt { m } } { n } \right)$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\mathrm { e } ^ { \mathrm { x } } + \ln \mathrm { x } = 7$

Write an equivalent expression in exponential form. - $\log _ { 4 } 1024 = 5$

Write an equation for the graph given. The graph represents an exponential function f with base 2 or 3, translated and/or reflected. -

Write the word or phrase that best completes each statement or answers the question. -Explain how the graph of $y = \log _ { 2 } ( x + 4 )$ an be obtained from the graph of y $y = \log _ { 2 } x$

Provide an appropriate response. -Give an equation of the form $f ( x ) = a ^ { x }$ to define the exponential function whose graph contains the point $( 2,16 )$ . Assume that $a > 0$ .

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\log ( x + 3 ) + 2 = x ^ { 2 } - 2 x + 1$

The graph of a function f is given. Use the graph to find the indicated value. -Let f(x) compute the time in hours to travel x miles at 60 miles per hour. What is the interpretation of $\mathrm { f } ^ { - 1 } ( 8 )$

Solve the equation and express the solution in exact form. - $\log _ { 2 } \sqrt { 2 x ^ { 2 } } = \frac { 5 } { 2 }$

Evaluate the logarithm. - $\log _ { 13 } ( - 1 )$

Solve the equation and express the solution in exact form. - $\ln ( 45 x - 5 ) = \ln 10$

Determine whether or not the function is one-to-one. - $f ( x ) = 7 x ^ { 3 } + 7$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Write an equivalent expression in exponential form. - log⁡1/2(x+4)=−5\log _ { 1 / 2 } ( x + 4 ) = - 5log1/2​(x+4)=−5

Use properties of logarithms to evaluate the expression. -If f(x)=log⁡6xf ( x ) = \log _ { 6 } xf(x)=log6​x , find f(66log⁡66)f \left( 6 ^ { 6 \log _ { 6 } 6 } \right)f(66log6​6)

Determine whether the statement is true or false. -The function f f(x)=mx+bf ( x ) = m x + bf(x)=mx+b b is a one-to-one function for all values of m and b.

Match the function with its graph. - f(x)=log⁡33xf ( x ) = \log _ { 3 } 3 xf(x)=log3​3x

Solve the equation. - (87)x=4964\left( \frac { 8 } { 7 } \right) ^ { x } = \frac { 49 } { 64 }(78​)x=6449​

Graph the function. - f(x)=(12)xf(x)=\left(\frac{1}{2}\right)^{x}f(x)=(21​)x

Solve the problem. -Given that f(x)=ex−1+3f ( x ) = e ^ { x - 1 } + 3f(x)=ex−1+3 , find f−1(x)f ^ { - 1 } ( x )f−1(x) and give the domain and range of f−1(x)f ^ { - 1 } ( x )f−1(x)

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - log⁡19(10mn)\log _ { 19 } \left( \frac { 10 \sqrt { m } } { n } \right)log19​(n10m​​)

Solve the following graphically. If necessary, round answers to the nearest thousandth. - ex+ln⁡x=7\mathrm { e } ^ { \mathrm { x } } + \ln \mathrm { x } = 7ex+lnx=7

Write an equivalent expression in exponential form. - log⁡41024=5\log _ { 4 } 1024 = 5log4​1024=5