Question 1

Simplify the expression   .

Accepted Answer

A) The expression cannot be simplified. 
B) 2 
C) 3 
D) -3 
E) -9 
A) The expression cannot be simplified. 
B) 2 
C) 3 
D) -3 
E) -9

Question 2

Use a calculator to find a value for   to four decimal places.

Accepted Answer

A) 1.0719 
B) -1.0719 
C) 2.4681 
D) 4.7707 
E) -2.4681 
A) 1.0719 
B) -1.0719 
C) 2.4681 
D) 4.7707 
E) -2.4681

Question 3

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

Accepted Answer

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

Question 4

Assume that x, y, and z are positive numbers. Use the properties of logarithms to write the expression   as the logarithm of one quantity.

Accepted Answer

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

Question 5

Identify the graph of the function.

Accepted Answer

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

Question 6

Assume that x, y, and a 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 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

A) 3.738 
B) 0.521 
C) 1.921 
D) 7.273 
E) 1.623 
A) 3.738 
B) 0.521 
C) 1.921 
D) 7.273 
E) 1.623

Question 9

Identify the x-intercept of the function   .

Accepted Answer

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

Question 10

Use a calculator to find a value for   to four decimal places.

Accepted Answer

A) -2.7788 
B) 2.7788 
C) -1.2068 
D) 1.2068 
E) 5.0814 
A) -2.7788 
B) 2.7788 
C) -1.2068 
D) 1.2068 
E) 5.0814

Question 11

Evaluate the function   at   . Round to 3 decimal places.

Accepted Answer

A) 4.190 
B) 4.590 
C) 14.611 
D) 5.412 
E) 2.890 
A) 4.190 
B) 4.590 
C) 14.611 
D) 5.412 
E) 2.890

Question 12

Find the graph of the function.

Accepted Answer

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

Question 13

What is the value of the function   at   ? Round to 3 decimal places.

Accepted Answer

A) 76.822 
B) 136.659 
C) 451.920 
D) 163.610 
E) 38.606 
A) 76.822 
B) 136.659 
C) 451.920 
D) 163.610 
E) 38.606

Question 14

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

Accepted Answer

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

Question 15

Assume that x, y, and c 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 16

Assume that x is a positive number. Use the properties of logarithms to write the expression   as the logarithm of one quantity.

Accepted Answer

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

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 5% per year, how long will it take the population of the town to triple?

Accepted Answer

A) 1.6 years 
B) 22 years 
C) 0.7 years 
D) 9.5 years 
E) 4.8 years 
A) 1.6 years 
B) 22 years 
C) 0.7 years 
D) 9.5 years 
E) 4.8 years

Question 18

Rewrite the logarithm   in terms of the natural logarithm.

Accepted Answer

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

Question 19

Condense the expression   to the logarithm of a single term.

Accepted Answer

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

Question 20

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

Accepted Answer

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

Simplify the expression .

Use a calculator to find a value for to four decimal places.

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

Assume that x, y, and z are positive numbers. Use the properties of logarithms to write the expression as the logarithm of one quantity.

Identify the graph of the function.

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

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

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

Identify the x-intercept of the function .

Use a calculator to find a value for to four decimal places.

Evaluate the function at . Round to 3 decimal places.

Find the graph of the function.

What is the value of the function at ? Round to 3 decimal places.

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

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

Assume that x is a positive number. Use the properties of logarithms to write the expression as the logarithm of one quantity.

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 5% per year, how long will it take the population of the town to triple?

Rewrite the logarithm in terms of the natural logarithm.

Condense the expression to the logarithm of a single term.

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

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

Simplify the expression .

Use a calculator to find a value for to four decimal places.

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

Assume that x, y, and z are positive numbers. Use the properties of logarithms to write the expression as the logarithm of one quantity.

Identify the graph of the function.

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

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

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

Identify the x-intercept of the function .

Use a calculator to find a value for to four decimal places.

Evaluate the function at . Round to 3 decimal places.

Find the graph of the function.

What is the value of the function at ? Round to 3 decimal places.

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

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

Assume that x is a positive number. Use the properties of logarithms to write the expression as the logarithm of one quantity.

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 5% per year, how long will it take the population of the town to triple?

Rewrite the logarithm in terms of the natural logarithm.

Condense the expression to the logarithm of a single term.

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

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 indicated.

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