Question 1

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) ​  ​

Accepted Answer

A) 3log8 x + 3log8 y + 3log8 z 
B) 3log8 x + 3log8 y - 3log8 z 
C)   
D) 3log8 x - 3log8 y - 3log8 z 
E) 3log8 x - 3log8 y + 3log8 z

Question 2

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) ​
Ln 9x
​

Accepted Answer

A) ln 9 - ln x 
B)   
C) ln 9 × ln x 
D) ln 9 + ln x 
E) None of these

Question 3

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​
Function
Value   ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Rewrite the logarithmic equation  in exponential form.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

Evaluate the function  at  without using a calculator.

Accepted Answer

A) 0 
B) -1 
C) -2 
D) 2 
E)

Question 7

Use the One-to-One Property to solve the equation for x. ​  ​

Accepted Answer

A) 11 
B) 14 
C) 12 
D) 13 
E) 10

Question 8

An initial investment of $5000 doubles in value in 6.3 years.Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

Accepted Answer

A) 11.0% 
B) 4.8% 
C) 5.5% 
D) 6.3% 
E) 100%

Question 9

A population growing at an annual rate r will triple in a time t given by the formula  .If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple? ​

Accepted Answer

A) 2.2 years 
B) 5.3 years 
C) 6.6 years 
D) 1 years 
E) 12.2 years

Question 10

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

Write the logarithmic equation in exponential form. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

Determine whether the given x-value is a solution (or an approximate solution) of the equation. ​  ​

Accepted Answer

A) No 
B) Yes

Question 15

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

Select the correct graph for the given function ​  ​

Accepted Answer

A) ​  
B) ​ ​  
C) ​  
D) ​  
E) ​

Question 17

Solve for x.Approximate the result to three decimal places. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio.
​  ​

Accepted Answer

A)    
B)    
C)    
D)    
E)

Question 19

Rewrite the logarithm as a ratio of common logarithms. ​
Log5 16
​

Accepted Answer

A)   
B)   
C)   
D)   
E) None of these

Question 20

Evaluate the function at the indicated value of  . ​  ​

Accepted Answer

A) 0 
B)   
C)   
D) -2 
E) 2

Exam 5: Exponential-And-Logarithmic-Functions

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.)

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) Ln 9x

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Rewrite the logarithmic equation in exponential form.

Evaluate the function at without using a calculator.

Use the One-to-One Property to solve the equation for x.

An initial investment of $5000 doubles in value in 6.3 years.Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

A population growing at an annual rate r will triple in a time t given by the formula .If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple?

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Write the logarithmic equation in exponential form.

Determine whether the given x-value is a solution (or an approximate solution) of the equation.

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Select the correct graph for the given function

Solve for x.Approximate the result to three decimal places.

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio.

Rewrite the logarithm as a ratio of common logarithms. Log₅ 16

Evaluate the function at the indicated value of .

Exam 5: Exponential-And-Logarithmic-Functions

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) ​ ​

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) ​ Ln 9x ​

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​ Function Value ​

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​ ​

Rewrite the logarithmic equation in exponential form.

Evaluate the function at without using a calculator.

Use the One-to-One Property to solve the equation for x. ​ ​

An initial investment of $5000 doubles in value in 6.3 years.Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

A population growing at an annual rate r will triple in a time t given by the formula .If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple? ​

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​ ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​ ​

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​ ​

Write the logarithmic equation in exponential form. ​ ​

Determine whether the given x-value is a solution (or an approximate solution) of the equation. ​ ​

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​ ​

Select the correct graph for the given function ​ ​

Solve for x.Approximate the result to three decimal places. ​ ​

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio. ​ ​

Rewrite the logarithm as a ratio of common logarithms. ​ Log5 16 ​

Evaluate the function at the indicated value of . ​ ​

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.)

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) Ln 9x

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Use the One-to-One Property to solve the equation for x.

A population growing at an annual rate r will triple in a time t given by the formula .If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple?

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Write the logarithmic equation in exponential form.

Determine whether the given x-value is a solution (or an approximate solution) of the equation.

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Select the correct graph for the given function

Solve for x.Approximate the result to three decimal places.

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio.

Rewrite the logarithm as a ratio of common logarithms. Log₅ 16

Evaluate the function at the indicated value of .