Question 1

Identify the value of the function   at   . Round to 3 decimal places.

Accepted Answer

A) 2.618 
B) 3.118 
C) 3.618 
D) 4.118 
E) 6.028 
A) 2.618 
B) 3.118 
C) 3.618 
D) 4.118 
E) 6.028

Question 2

Evaluate the logarithm   using the change of base formula. Round to 3 decimal places.

Accepted Answer

A) -12.354 
B) 0.089 
C) 0.039 
D) -0.098 
E) -0.081 
A) -12.354 
B) 0.089 
C) 0.039 
D) -0.098 
E) -0.081

Question 3

Find the exact value of   without using a calculator.

Accepted Answer

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

Question 4

Assume that x, y, and b are positive numbers. Use the properties of logarithms to write the expression   in terms of the logarithms of x and y.

Accepted Answer

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

Question 5

Identify the x-intercept of the function   .

Accepted Answer

A)    
B)    
C)    
D) The function has no x-intercept. 
E)    
A)    
B)    
C)    
D) The function has no x-intercept. 
E)

Question 6

Graph the exponential function.

Accepted Answer

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

Question 7

Condense the expression   to the logarithm of a single term.

Accepted Answer

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

Question 8

Find the value of b that would cause the graph of y = bx to look like the graph below.

Accepted Answer

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

Question 9

Use a graphing utility to determine which graph below is the graph of the function.

Accepted Answer

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

Question 10

Rewrite the logarithm   in terms of the common logarithm (base 10).

Accepted Answer

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

Question 11

Find the exact value of   without using a calculator.

Accepted Answer

A) 1.25 
B) 2 
C) 3 
D) 2.5 
E) 5 
A) 1.25 
B) 2 
C) 3 
D) 2.5 
E) 5

Question 12

Condense the expression   to the logarithm of a single term.

Accepted Answer

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

Question 13

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 15% per year, how long will it take the population of the town to triple?

Accepted Answer

A) 8.1 years 
B) 3.2 years 
C) 2.7 years 
D) 7.3 years 
E) 1.2 years 
A) 8.1 years 
B) 3.2 years 
C) 2.7 years 
D) 7.3 years 
E) 1.2 years

Question 14

Write the equation   in logarithmic form.

Accepted Answer

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

Question 15

Condense the expression   to the logarithm of a single term.

Accepted Answer

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

Question 16

Find the value of b, if any, that would cause the graph of   to look like the graph shown.

Accepted Answer

A) b = 3.4 
B) b = 2 
C) b = -1 
D) b = 4 
E) b = 4.6 
A) b = 3.4 
B) b = 2 
C) b = -1 
D) b = 4 
E) b = 4.6

Question 17

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

Question 18

Graph the function using translations.

Accepted Answer

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

Question 19

Rewrite the exponential equation   in logarithmic form.

Accepted Answer

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

Question 20

Graph the function using translations.

Accepted Answer

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

Identify the value of the function at . Round to 3 decimal places.

Evaluate the logarithm using the change of base formula. Round to 3 decimal places.

Find the exact value of without using a calculator.

Assume that x, y, and b are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x and y.

Identify the x-intercept of the function .

Graph the exponential function.

Condense the expression to the logarithm of a single term.

Find the value of b that would cause the graph of y = b^x to look like the graph below.

Use a graphing utility to determine which graph below is the graph of the function.

Rewrite the logarithm in terms of the common logarithm (base 10).

Find the exact value of without using a calculator.

Condense the expression to the logarithm of a single term.

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 15% per year, how long will it take the population of the town to triple?

Write the equation in logarithmic form.

Condense the expression to the logarithm of a single term.

Find the value of b, if any, that would cause the graph of to look like the graph shown.

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?

Graph the function using translations.

Rewrite the exponential equation in logarithmic form.

Graph the function using translations.

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Algebraic Expressions and Equations

Filters

Exam 4: Exponential and Logarithmic Functions

Identify the value of the function at . Round to 3 decimal places.

Evaluate the logarithm using the change of base formula. Round to 3 decimal places.

Find the exact value of without using a calculator.

Assume that x, y, and b are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x and y.

Identify the x-intercept of the function .

Graph the exponential function.

Condense the expression to the logarithm of a single term.

Find the value of b that would cause the graph of y = bx to look like the graph below.

Use a graphing utility to determine which graph below is the graph of the function.

Rewrite the logarithm in terms of the common logarithm (base 10).

Find the exact value of without using a calculator.

Condense the expression to the logarithm of a single term.

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 15% per year, how long will it take the population of the town to triple?

Write the equation in logarithmic form.

Condense the expression to the logarithm of a single term.

Find the value of b, if any, that would cause the graph of to look like the graph shown.

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?

Graph the function using translations.

Rewrite the exponential equation in logarithmic form.

Graph the function using translations.

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Algebraic Expressions and Equations

Filters

Find the value of b that would cause the graph of y = b^x to look like the graph below.