Question 1

Use the exponential growth formula to find the final amount. Round to the nearest whole.
-

Accepted Answer

A)  225 
B)  689 
C)  691 
D)  641 
A)  225 
B)  689 
C)  691 
D)  641

Question 2

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

Accepted Answer

A)  1 
B)  3 
C)  0 
D)  $\frac { 1 } { 3 }$ 
A)  1 
B)  3 
C)  0 
D)  $\frac { 1 } { 3 }$

Question 3

Solve the equation.
-$$\log _ { 7 } \left( x ^ { 2 } - 6 x \right) = 1$$

Accepted Answer

A)  $\{ 7 , - 1 \}$ 
B)  $\{ 7 \}$ 
C)  $\{ - 7,1 \}$ 
D)  $\{ 1 \}$ 
A)  $\{ 7 , - 1 \}$ 
B)  $\{ 7 \}$ 
C)  $\{ - 7,1 \}$ 
D)  $\{ 1 \}$

Question 4

Find the inverse of the one-to-one function.
-$$f ( x ) = \frac { 8 x + 5 } { 7 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { 7 } { 8 x + 5 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 7 x - 5 } { 8 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 7 \mathrm { x } + 5 } { 8 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 7 } { 8 x - 5 }$ 
A)  $f ^ { - 1 } ( x ) = \frac { 7 } { 8 x + 5 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 7 x - 5 } { 8 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 7 \mathrm { x } + 5 } { 8 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 7 } { 8 x - 5 }$

Question 5

Solve the equation for x. Give an exact solution.
-$\log x = 2.2$

Accepted Answer

A)  $\left\{ 10 ^ { 2.2 } \right\}$ 
B)  $\left\{ \mathrm { e } ^ { 2.2 } \right\}$ 
C)  $\left\{ 2.2 ^ { 10 } \right\}$ 
D)  $\{ 2.2 \mathrm { e } \}$ 
A)  $\left\{ 10 ^ { 2.2 } \right\}$ 
B)  $\left\{ \mathrm { e } ^ { 2.2 } \right\}$ 
C)  $\left\{ 2.2 ^ { 10 } \right\}$ 
D)  $\{ 2.2 \mathrm { e } \}$

Question 6

Solve. Round the answer to the nearest whole.
-Suppose a city with population of 170,000 has been decreasing at a rate of 3% per year. If this rate continues, predict the population of the city in 20 years.

Accepted Answer

A)  92,445 
B)  113,493 
C)  307,039 
D)  75,140 
A)  92,445 
B)  113,493 
C)  307,039 
D)  75,140

Question 7

Use the exponential growth formula to find the final amount. Round to the nearest whole.
-

Accepted Answer

A)  77,150 
B)  54,288 
C)  56,205 
D)  34 
A)  77,150 
B)  54,288 
C)  56,205 
D)  34

Question 8

Solve the equation for x. Give an exact solution.
-$\log ( 3 x + 8 ) = - 0.3$

Accepted Answer

A)  $\left\{ \frac { 10 ^ { - 0.3 } - 8 } { 3 } \right\}$ 
B)  $\left\{ 10 ^ { - 0.3 } - 8 \right\}$ 
C)  $\left\{ 3 \left( 10 ^ { - 0.3 } - 8 \right) \right\}$ 
D)  $\left\{ \frac { 10 ^ { - 0.3 } + 3 } { 8 } \right\}$ 
A)  $\left\{ \frac { 10 ^ { - 0.3 } - 8 } { 3 } \right\}$ 
B)  $\left\{ 10 ^ { - 0.3 } - 8 \right\}$ 
C)  $\left\{ 3 \left( 10 ^ { - 0.3 } - 8 \right) \right\}$ 
D)  $\left\{ \frac { 10 ^ { - 0.3 } + 3 } { 8 } \right\}$

Question 9

Solve for x.
-$$\log _ { 3 } \frac { 1 } { 9 } = x$$

Accepted Answer

A)  $\{ - 2 \}$ 
B)  $\left\{ \frac { 1 } { 27 } \right\}$ 
C)  $\{ 2 \}$ 
D)  $\left\{ \frac { 1 } { 3 } \right\}$ 
A)  $\{ - 2 \}$ 
B)  $\left\{ \frac { 1 } { 27 } \right\}$ 
C)  $\{ 2 \}$ 
D)  $\left\{ \frac { 1 } { 3 } \right\}$

Question 10

Solve the equation. Give an approximate solution to four decimal places.
-$$4 ^ { x } = 11$$

Accepted Answer

A)  $\{ 0.3636 \}$ 
B)  $\{ 1.7297 \}$ 
C)  $\{ 3.3242 \}$ 
D)  $\{ 0.5781 \}$ 
A)  $\{ 0.3636 \}$ 
B)  $\{ 1.7297 \}$ 
C)  $\{ 3.3242 \}$ 
D)  $\{ 0.5781 \}$

Question 11

Graph the inverse of the function on the same set of axes.
-

Accepted Answer

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

Question 12

Solve the equation.
-$\log _ { 72 } \left( x ^ { 2 } - x \right) = 1$

Accepted Answer

A)  $\{ - 8,9 \}$ 
B)  $\{ 1,72 \}$ 
C)  $\{ - 8 , - 9 \}$ 
D)  $\{ 8,9 \}$ 
A)  $\{ - 8,9 \}$ 
B)  $\{ 1,72 \}$ 
C)  $\{ - 8 , - 9 \}$ 
D)  $\{ 8,9 \}$

Question 13

Graph the one-to-one function and its inverse on the same set of axes.
-$f(x)=6 x-19$

Accepted Answer

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

Question 14

Solve for x.
-$$\log _ { 2 } x = 3$$

Accepted Answer

A)  $\{ 8 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 9 \}$ 
D)  $\{ 5 \}$ 
A)  $\{ 8 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 9 \}$ 
D)  $\{ 5 \}$

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Write the expression as sums or differences of multiples of logarithms.
-$\log _ { 5 } \frac { x - 3 } { x ^ { 3 } }$

Accepted Answer

A)  $\log _ { 5 } ( x - 3 ) - \log _ { 5 } x$ 
B)  $3 \log _ { 5 } x - \log _ { 5 } ( x - 3 )$ 
C)  $\log _ { 5 } ( x - 3 ) + 3 \log _ { 5 } x$ 
D)  $\log _ { 5 } ( x - 3 ) - 3 \log _ { 5 } x$ 
A)  $\log _ { 5 } ( x - 3 ) - \log _ { 5 } x$ 
B)  $3 \log _ { 5 } x - \log _ { 5 } ( x - 3 )$ 
C)  $\log _ { 5 } ( x - 3 ) + 3 \log _ { 5 } x$ 
D)  $\log _ { 5 } ( x - 3 ) - 3 \log _ { 5 } x$

Question 18

Write as an exponential equation.
-$\log _ { 1.1 } 1.21 = 2$

Accepted Answer

A)  $2 ^ { 1.1 } = 1.21$ 
B)  $1.1 ^ { 1.21 } = 2$ 
C)  $1.21 ^ { 2 } = 1.1$ 
D)  $1.1 ^ { 2 } = 1.21$ 
A)  $2 ^ { 1.1 } = 1.21$ 
B)  $1.1 ^ { 1.21 } = 2$ 
C)  $1.21 ^ { 2 } = 1.1$ 
D)  $1.1 ^ { 2 } = 1.21$

Question 19

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

Accepted Answer

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

Question 20

Write as a logarithmic equation.
-$$5 ^ { 3 } = 125$$

Accepted Answer

A)  $\log _ { 5 } 3 = 125$ 
B)  $\log _ { 5 } 125 = 3$ 
C)  $\log _ { 125 } 5 = 3$ 
D)  $\log _ { 3 } 125 = 5$ 
A)  $\log _ { 5 } 3 = 125$ 
B)  $\log _ { 5 } 125 = 3$ 
C)  $\log _ { 125 } 5 = 3$ 
D)  $\log _ { 3 } 125 = 5$

Use the exponential growth formula to find the final amount. Round to the nearest whole. -

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

Solve the equation. - $\log _ { 7 } \left( x ^ { 2 } - 6 x \right) = 1$

Find the inverse of the one-to-one function. - $f ( x ) = \frac { 8 x + 5 } { 7 }$

Solve the equation for x. Give an exact solution. - $\log x = 2.2$

Solve. Round the answer to the nearest whole. -Suppose a city with population of 170,000 has been decreasing at a rate of 3% per year. If this rate continues, predict the population of the city in 20 years.

Use the exponential growth formula to find the final amount. Round to the nearest whole. -

Solve the equation for x. Give an exact solution. - $\log ( 3 x + 8 ) = - 0.3$

Solve for x. - $\log _ { 3 } \frac { 1 } { 9 } = x$

Solve the equation. Give an approximate solution to four decimal places. - $4 ^ { x } = 11$

Graph the inverse of the function on the same set of axes. -

Solve the equation. - $\log _ { 72 } \left( x ^ { 2 } - x \right) = 1$

Graph the one-to-one function and its inverse on the same set of axes. - $f(x)=6 x-19$

Solve for x. - $\log _ { 2 } x = 3$

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

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

Write the expression as sums or differences of multiples of logarithms. - $\log _ { 5 } \frac { x - 3 } { x ^ { 3 } }$

Write as an exponential equation. - $\log _ { 1.1 } 1.21 = 2$

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

Write as a logarithmic equation. - $5 ^ { 3 } = 125$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Fractions

Filters

Exam 9: Exponential and Logarithmic Functions

Use the exponential growth formula to find the final amount. Round to the nearest whole. -

Find the value of the logarithmic expression. - log⁡33\log _ { 3 } 3log3​3

Solve the equation. - log⁡7(x2−6x)=1\log _ { 7 } \left( x ^ { 2 } - 6 x \right) = 1log7​(x2−6x)=1

Find the inverse of the one-to-one function. - f(x)=8x+57f ( x ) = \frac { 8 x + 5 } { 7 }f(x)=78x+5​

Solve the equation for x. Give an exact solution. - log⁡x=2.2\log x = 2.2logx=2.2

Solve. Round the answer to the nearest whole. -Suppose a city with population of 170,000 has been decreasing at a rate of 3% per year. If this rate continues, predict the population of the city in 20 years.

Use the exponential growth formula to find the final amount. Round to the nearest whole. -

Solve the equation for x. Give an exact solution. - log⁡(3x+8)=−0.3\log ( 3 x + 8 ) = - 0.3log(3x+8)=−0.3

Solve for x. - log⁡319=x\log _ { 3 } \frac { 1 } { 9 } = xlog3​91​=x

Solve the equation. Give an approximate solution to four decimal places. - 4x=114 ^ { x } = 114x=11

Graph the inverse of the function on the same set of axes. -

Solve the equation. - log⁡72(x2−x)=1\log _ { 72 } \left( x ^ { 2 } - x \right) = 1log72​(x2−x)=1

Graph the one-to-one function and its inverse on the same set of axes. - f(x)=6x−19f(x)=6 x-19f(x)=6x−19

Solve for x. - log⁡2x=3\log _ { 2 } x = 3log2​x=3

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

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

Write the expression as sums or differences of multiples of logarithms. - log⁡5x−3x3\log _ { 5 } \frac { x - 3 } { x ^ { 3 } }log5​x3x−3​

Write as an exponential equation. - log⁡1.11.21=2\log _ { 1.1 } 1.21 = 2log1.1​1.21=2

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

Write as a logarithmic equation. - 53=1255 ^ { 3 } = 12553=125

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Fractions

Filters

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

Solve the equation. - $\log _ { 7 } \left( x ^ { 2 } - 6 x \right) = 1$

Find the inverse of the one-to-one function. - $f ( x ) = \frac { 8 x + 5 } { 7 }$

Solve the equation for x. Give an exact solution. - $\log x = 2.2$

Solve the equation for x. Give an exact solution. - $\log ( 3 x + 8 ) = - 0.3$

Solve for x. - $\log _ { 3 } \frac { 1 } { 9 } = x$

Solve the equation. Give an approximate solution to four decimal places. - $4 ^ { x } = 11$

Solve the equation. - $\log _ { 72 } \left( x ^ { 2 } - x \right) = 1$

Graph the one-to-one function and its inverse on the same set of axes. - $f(x)=6 x-19$

Solve for x. - $\log _ { 2 } x = 3$

Write the expression as sums or differences of multiples of logarithms. - $\log _ { 5 } \frac { x - 3 } { x ^ { 3 } }$

Write as an exponential equation. - $\log _ { 1.1 } 1.21 = 2$

Write as a logarithmic equation. - $5 ^ { 3 } = 125$