Question 1

Solve the equation.
-$$2 ^ { x } = \frac { 1 } { 8 }$$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 1 } { 3 } \right\}$ 
C)  $\left\{ \frac { 1 } { 4 } \right\}$ 
D)  $\{ - 3 \}$ 
A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 1 } { 3 } \right\}$ 
C)  $\left\{ \frac { 1 } { 4 } \right\}$ 
D)  $\{ - 3 \}$ D

Question 2

Solve the equation.
-$$\log _ { 2 } ( 3 x - 2 ) - \log _ { 2 } ( x - 5 ) = 4$$

Accepted Answer

A)  $\{ 6 \}$ 
B)  $\left\{ \frac { 3 } { 13 } \right\}$ 
C)  $\left\{ \frac { 38 } { 5 } \right\}$ 
D)  $\{ 18 \}$ 
A)  $\{ 6 \}$ 
B)  $\left\{ \frac { 3 } { 13 } \right\}$ 
C)  $\left\{ \frac { 38 } { 5 } \right\}$ 
D)  $\{ 18 \}$ A

Question 3

Solve the problem.
-Kimberly invested $3000 in her savings account for 7 years. When she withdrew it, she had $3779.58. Interest was compounded continuously. What was the interest rate on the account? Round to the nearest tenth of a percent.

Accepted Answer

A) 3.3% 
B) 3.2% 
C) 3.45% 
D) 3.4% 
A) 3.3% 
B) 3.2% 
C) 3.45% 
D) 3.4% A

Question 4

Graph the function.
-$$( x ) = - \frac { 1 } { 2 } \log _ { 5 } x$$

Accepted Answer

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

Question 5

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator.
-$\log 10,000$

Accepted Answer

A)  $\frac { 1 } { 10000 }$ 
B)  40 
C)  $- 4$ 
D)  4 
A)  $\frac { 1 } { 10000 }$ 
B)  40 
C)  $- 4$ 
D)  4

Question 6

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
-$\log _ { b } \frac { x y ^ { 3 } } { z ^ { 6 } }$

Accepted Answer

A)  $\log _ { b } x + \log _ { b } y ^ { 3 } - \log _ { b } z ^ { 6 }$ 
B)  $\log _ { b } x + 3 \log _ { b } y + 6 \log _ { b } z$ 
C)  $\log _ { b } x + \log _ { b } \mathrm { y } ^ { 3 } + \log _ { \mathrm { b } } \mathrm { z } ^ { 6 }$ 
D)  $\log _ { \mathrm { b } } \mathrm { x } + 3 \log _ { \mathrm { b } } \mathrm { y } - 6 \log _ { \mathrm { b } } \mathrm { z }$ 
A)  $\log _ { b } x + \log _ { b } y ^ { 3 } - \log _ { b } z ^ { 6 }$ 
B)  $\log _ { b } x + 3 \log _ { b } y + 6 \log _ { b } z$ 
C)  $\log _ { b } x + \log _ { b } \mathrm { y } ^ { 3 } + \log _ { \mathrm { b } } \mathrm { z } ^ { 6 }$ 
D)  $\log _ { \mathrm { b } } \mathrm { x } + 3 \log _ { \mathrm { b } } \mathrm { y } - 6 \log _ { \mathrm { b } } \mathrm { z }$

Question 7

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
-$\operatorname { og } ( 1000 x )$

Accepted Answer

A)  $3 x$ 
B)  $3 \log x$ 
C)  $3 + \log x$ 
D)  $30 + \log x$ 
A)  $3 x$ 
B)  $3 \log x$ 
C)  $3 + \log x$ 
D)  $30 + \log x$

Question 8

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$$\log _ { \mathrm { c } } \mathrm { x } + \log _ { \mathrm { c } } \mathrm { y }$$

Accepted Answer

A)  $\log _ { C } \mathrm { x } \cdot \log _ { \mathrm { c } } \mathrm { y }$ 
B)  $\log _ { \mathrm { C } } \left( \frac { \mathrm { x } } { \mathrm { V } } \right)$ 
C)  $\log _ { \mathrm { C } } ( \mathrm { xy } )$ 
D)  $\log _ { \mathrm { C } } ( \mathrm { x } + \mathrm { y } )$ 
A)  $\log _ { C } \mathrm { x } \cdot \log _ { \mathrm { c } } \mathrm { y }$ 
B)  $\log _ { \mathrm { C } } \left( \frac { \mathrm { x } } { \mathrm { V } } \right)$ 
C)  $\log _ { \mathrm { C } } ( \mathrm { xy } )$ 
D)  $\log _ { \mathrm { C } } ( \mathrm { x } + \mathrm { y } )$

Question 9

Write the exponential equation as an equation involving a logarithm.
-$$4 ^ { 5 / 2 } = 32$$

Accepted Answer

A)  $\log _ { 32 } 4 = \frac { 5 } { 2 }$ 
B)  $\log _ { 4 } 32 = \frac { 5 } { 2 }$ 
C)  $\frac { \log _ { 2 } 32 } { \log _ { 5 } 4 } = 4$ 
D)  $\log _ { 5 } 4 = \frac { 5 } { 2 }$ 
A)  $\log _ { 32 } 4 = \frac { 5 } { 2 }$ 
B)  $\log _ { 4 } 32 = \frac { 5 } { 2 }$ 
C)  $\frac { \log _ { 2 } 32 } { \log _ { 5 } 4 } = 4$ 
D)  $\log _ { 5 } 4 = \frac { 5 } { 2 }$

Question 10

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function.
-$$f ( x ) = 3 ^ { - x } + 4$$

Accepted Answer

A)  domain: $( - \infty , \infty )$; range: $( 4 , \infty )$
 horizontal asymptote: $\mathrm { y } = 4$
  
B)  domain: $( - \infty , \infty )$; range: $( 3 , \infty )$
 horizontal asymptote: $\mathrm { y } = 3$
  
C)  domain: $( - \infty , \infty )$; range: $( 3 , \infty )$
horizontal asymptote: $y = 3$ 
  
D)  domain: $( - \infty , \infty )$; range: $( 4 , \infty )$ 
horizontal asymptote: $y = 4$
  
A)  domain: $( - \infty , \infty )$; range: $( 4 , \infty )$
 horizontal asymptote: $\mathrm { y } = 4$
  
B)  domain: $( - \infty , \infty )$; range: $( 3 , \infty )$
 horizontal asymptote: $\mathrm { y } = 3$
  
C)  domain: $( - \infty , \infty )$; range: $( 3 , \infty )$
horizontal asymptote: $y = 3$ 
  
D)  domain: $( - \infty , \infty )$; range: $( 4 , \infty )$ 
horizontal asymptote: $y = 4$

Question 11

Solve the equation.
-$$4 ^{( 1 + 2 x )} = 1024$$

Accepted Answer

A)  $\{ - 2 \}$ 
B)  $\{ 8 \}$ 
C)  $\{ 256 \}$ 
D)  $\{ 2 \}$ 
A)  $\{ - 2 \}$ 
B)  $\{ 8 \}$ 
C)  $\{ 256 \}$ 
D)  $\{ 2 \}$

Question 12

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator.
-ln l

Accepted Answer

A) -1 
B) 1 
C) 0 
D) e 
A) -1 
B) 1 
C) 0 
D) e

Question 13

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$$\frac { 1 } { 7 } \left[ 3 \ln ( x + 6 ) - \ln x - \ln \left( x ^ { 2 } - 4 \right) \right]$$

Accepted Answer

A)  $\ln \sqrt [ 7 ] { \frac { ( x + 6 ) ^ { 3 } } { x \left( x ^ { 2 } - 4 \right) } }$ 
B)  $\ln \sqrt [ 7 ] { \frac { x ( x + 6 ) ^ { 3 } } { \left( x ^ { 2 } - 4 \right) } }$ 
C)  $\ln \sqrt [ 7 ] { \frac { 3 ( x + 6 ) } { x \left( x ^ { 2 } - 4 \right) } }$ 
D)  $\ln \sqrt [ 7 ] { \frac { ( x + 6 ) ^ { 3 } \left( x ^ { 2 } - 4 \right) } { x } }$ 
A)  $\ln \sqrt [ 7 ] { \frac { ( x + 6 ) ^ { 3 } } { x \left( x ^ { 2 } - 4 \right) } }$ 
B)  $\ln \sqrt [ 7 ] { \frac { x ( x + 6 ) ^ { 3 } } { \left( x ^ { 2 } - 4 \right) } }$ 
C)  $\ln \sqrt [ 7 ] { \frac { 3 ( x + 6 ) } { x \left( x ^ { 2 } - 4 \right) } }$ 
D)  $\ln \sqrt [ 7 ] { \frac { ( x + 6 ) ^ { 3 } \left( x ^ { 2 } - 4 \right) } { x } }$

Question 14

Solve the problem.
-The formula $\mathrm { P } = 14.7 \mathrm { e } ^ { - 0.21 \mathrm { x } }$ gives the average atmospheric pressure, $\mathrm { P }$, in pounds per square inch, at an altitude $x$, in miles above sea level. Find the average atmospheric pressure for an altitude of $2.3$ miles. Round your answer to the nearest tenth.

Accepted Answer

A)  $9.1 \mathrm { lb } /$ in. $^ { 2 }$ 
B)  $11.0 \mathrm { lb } / \mathrm { in } ^ { 2 }$ 
C)  $8.4 \mathrm { lb } / \mathrm { in } ^ { 2 }$ 
D)  $7.8 \mathrm { lb } /$ in. $^ { 2 }$ 
A)  $9.1 \mathrm { lb } /$ in. $^ { 2 }$ 
B)  $11.0 \mathrm { lb } / \mathrm { in } ^ { 2 }$ 
C)  $8.4 \mathrm { lb } / \mathrm { in } ^ { 2 }$ 
D)  $7.8 \mathrm { lb } /$ in. $^ { 2 }$

Question 15

Solve the problem.
-Laura borrows $5000 at a rate of 9% compounded monthly. Find how much Laura owes at the end of 4 years. Use: $A = P \left( 1 + \frac { r } { n } \right) ^ { \text {nt } }$ where:
$\mathrm { A } =$ final amount
$\mathrm { P } = \$ 5000$ (the amount borrowed)
$r = 9 \% = 0.09$ (the annual rate of interest)
$\mathrm { n } = 12$ (the number of times interest is compounded each year)
$t = 4$ (the duration of the loan in years)

Accepted Answer

A) $241,800.00 
B) $7157.03 
C) $7872.73 
D) $5151.70 
A) $241,800.00 
B) $7157.03 
C) $7872.73 
D) $5151.70

Question 16

Determine the correct exponential function of the form f(x) = bS1U1P1xS1S1P0 whose graph is given.
-

Accepted Answer

A)  $f ( x ) = - 12 ^ { x }$ 
B)  $f ( x ) = \left( \frac { 1 } { 64 } \right) ^ { x }$ 
C)  $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$ 
D)  $f ( x ) = - 3 ^ { x }$ 
A)  $f ( x ) = - 12 ^ { x }$ 
B)  $f ( x ) = \left( \frac { 1 } { 64 } \right) ^ { x }$ 
C)  $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$ 
D)  $f ( x ) = - 3 ^ { x }$

Question 17

Write the logarithmic equation as an exponential equation.
-$\ln x = 5$

Accepted Answer

A)  $e ^ { x } = 5$ 
B)  $e ^ { 5 } = x$ 
C)  $x ^ { 5 } = e$ 
D)  $5 ^ { \mathrm { e } } = \mathrm { x }$ 
A)  $e ^ { x } = 5$ 
B)  $e ^ { 5 } = x$ 
C)  $x ^ { 5 } = e$ 
D)  $5 ^ { \mathrm { e } } = \mathrm { x }$

Question 18

Determine the correct exponential function of the form f(x) = bS1U1P1xS1S1P0 whose graph is given.
-

Accepted Answer

A)  $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$ 
B)  $f ( x ) = - 3 ^ { x }$ 
C)  $f ( x ) = 4 ^ { x }$ 
D)  $f ( x ) = - 4 ^ { x }$ 
A)  $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$ 
B)  $f ( x ) = - 3 ^ { x }$ 
C)  $f ( x ) = 4 ^ { x }$ 
D)  $f ( x ) = - 4 ^ { x }$

Question 19

Determine the correct exponential function of the form f(x) = bS1U1P1xS1S1P0 whose graph is given.
-

Accepted Answer

A)  $f ( x ) = \left( \frac { 4 } { 5 } \right) ^ { x }$ 
B)  $f ( x ) = \left( \frac { 5 } { 4 } \right) ^ { x }$ 
C)  $f ( x ) = - 2 ^ { x }$ 
D)  $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }$ 
A)  $f ( x ) = \left( \frac { 4 } { 5 } \right) ^ { x }$ 
B)  $f ( x ) = \left( \frac { 5 } { 4 } \right) ^ { x }$ 
C)  $f ( x ) = - 2 ^ { x }$ 
D)  $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }$

Question 20

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$\log _ { 10 } 4 + \log _ { 10 } 25$

Accepted Answer

A)  $\log _ { 10 }100$ 
B)  $2 \log _ { 10 } 10$ 
C)  2 
D)  $\log _ { 10 ^ { 29 } }$ 
A)  $\log _ { 10 }100$ 
B)  $2 \log _ { 10 } 10$ 
C)  2 
D)  $\log _ { 10 ^ { 29 } }$

Solve the equation. - $2 ^ { x } = \frac { 1 } { 8 }$

Solve the equation. - $\log _ { 2 } ( 3 x - 2 ) - \log _ { 2 } ( x - 5 ) = 4$

Solve the problem. -Kimberly invested $3000 in her savings account for 7 years. When she withdrew it, she had $3779.58. Interest was compounded continuously. What was the interest rate on the account? Round to the nearest tenth of a percent.

Graph the function. - $( x ) = - \frac { 1 } { 2 } \log _ { 5 } x$ $Graph the function. - ( x ) = - \frac { 1 } { 2 } \log _ { 5 } x$

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator. - $\log 10,000$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { b } \frac { x y ^ { 3 } } { z ^ { 6 } }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\operatorname { og } ( 1000 x )$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log _ { \mathrm { c } } \mathrm { x } + \log _ { \mathrm { c } } \mathrm { y }$

Write the exponential equation as an equation involving a logarithm. - $4 ^ { 5 / 2 } = 32$

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - $f ( x ) = 3 ^ { - x } + 4$ $Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - f ( x ) = 3 ^ { - x } + 4$

Solve the equation. - $4 ^{( 1 + 2 x )} = 1024$

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator. -ln l

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\frac { 1 } { 7 } \left[ 3 \ln ( x + 6 ) - \ln x - \ln \left( x ^ { 2 } - 4 \right) \right]$

Determine the correct exponential function of the form f(x) = b^x whose graph is given. -

Write the logarithmic equation as an exponential equation. - $\ln x = 5$

Determine the correct exponential function of the form f(x) = b^x whose graph is given. -

Determine the correct exponential function of the form f(x) = b^x whose graph is given. -

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log _ { 10 } 4 + \log _ { 10 } 25$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 5: Exponential and Logarithmic Functions and Equations

Solve the equation. - 2x=182 ^ { x } = \frac { 1 } { 8 }2x=81​

Solve the equation. - log⁡2(3x−2)−log⁡2(x−5)=4\log _ { 2 } ( 3 x - 2 ) - \log _ { 2 } ( x - 5 ) = 4log2​(3x−2)−log2​(x−5)=4

Solve the problem. -Kimberly invested $3000 in her savings account for 7 years. When she withdrew it, she had $3779.58. Interest was compounded continuously. What was the interest rate on the account? Round to the nearest tenth of a percent.

Graph the function. - (x)=−12log⁡5x( x ) = - \frac { 1 } { 2 } \log _ { 5 } x(x)=−21​log5​x

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator. - log⁡10,000\log 10,000log10,000

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡bxy3z6\log _ { b } \frac { x y ^ { 3 } } { z ^ { 6 } }logb​z6xy3​

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - og⁡(1000x)\operatorname { og } ( 1000 x )og(1000x)

Write the exponential equation as an equation involving a logarithm. - 45/2=324 ^ { 5 / 2 } = 3245/2=32

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - f(x)=3−x+4f ( x ) = 3 ^ { - x } + 4f(x)=3−x+4

Solve the equation. - 4(1+2x)=10244 ^{( 1 + 2 x )} = 10244(1+2x)=1024

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator. -ln l

Determine the correct exponential function of the form f(x) = bx whose graph is given. -

Write the logarithmic equation as an exponential equation. - ln⁡x=5\ln x = 5lnx=5

Determine the correct exponential function of the form f(x) = bx whose graph is given. -

Determine the correct exponential function of the form f(x) = bx whose graph is given. -

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - log⁡104+log⁡1025\log _ { 10 } 4 + \log _ { 10 } 25log10​4+log10​25

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Solve the equation. - $2 ^ { x } = \frac { 1 } { 8 }$

Solve the equation. - $\log _ { 2 } ( 3 x - 2 ) - \log _ { 2 } ( x - 5 ) = 4$

Graph the function. - $( x ) = - \frac { 1 } { 2 } \log _ { 5 } x$ $Graph the function. - ( x ) = - \frac { 1 } { 2 } \log _ { 5 } x$

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator. - $\log 10,000$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { b } \frac { x y ^ { 3 } } { z ^ { 6 } }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\operatorname { og } ( 1000 x )$

Write the exponential equation as an equation involving a logarithm. - $4 ^ { 5 / 2 } = 32$

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - $f ( x ) = 3 ^ { - x } + 4$ $Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - f ( x ) = 3 ^ { - x } + 4$

Solve the equation. - $4 ^{( 1 + 2 x )} = 1024$

Determine the correct exponential function of the form f(x) = b^x whose graph is given. -

Write the logarithmic equation as an exponential equation. - $\ln x = 5$

Determine the correct exponential function of the form f(x) = b^x whose graph is given. -

Determine the correct exponential function of the form f(x) = b^x whose graph is given. -

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log _ { 10 } 4 + \log _ { 10 } 25$