Question 1

Solve the equation. 2x = 7

Accepted Answer

A) x = 1.3562 
B) x = 1.5907 
C) x = 0.3562 
D) x = 5.7883 
E) x = 0.4796 
A) x = 1.3562 
B) x = 1.5907 
C) x = 0.3562 
D) x = 5.7883 
E) x = 0.4796

Question 2

Simplify the expression   .

Accepted Answer

A) 4 
B) -12 
C) 1 
D) -108 
E) The expression cannot be simplified. 
A) 4 
B) -12 
C) 1 
D) -108 
E) The expression cannot be simplified.

Question 3

Condense the expression   to the logarithm of a single term.

Accepted Answer

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

Question 4

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 5

Graph the function using translations.

Accepted Answer

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

Question 6

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 7

Find the graph of the function.

Accepted Answer

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

Question 8

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 9

Condense the expression   to the logarithm of a single term.

Accepted Answer

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

Question 10

Rewrite the logarithmic equation   in exponential form.

Accepted Answer

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

Question 11

Graph the function using translations.

Accepted Answer

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

Question 12

An initial investment of $1000 grows at an annual interest rate of 7% compounded continuously. How long will it take to double the investment?

Accepted Answer

A) 10.29 years 
B) 9.29 years 
C) 9.90 years 
D) 10.90 years 
E) 1 year 
A) 10.29 years 
B) 9.29 years 
C) 9.90 years 
D) 10.90 years 
E) 1 year

Question 13

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

Accepted Answer

A) -1.6314 
B) 6.0591 
C) -3.7565 
D) 3.7565 
E) 1.6314 
A) -1.6314 
B) 6.0591 
C) -3.7565 
D) 3.7565 
E) 1.6314

Question 14

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 15

Graph the function.

Accepted Answer

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

Question 16

Simplify the expression.

Accepted Answer

A) 4 
B) 5 
C) 20 
D) 16 
E) none of these 
A) 4 
B) 5 
C) 20 
D) 16 
E) none of these

Question 17

The chemical acidity of a solution is measured in units of pH:   , where   is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.2, how many times higher is its   than pure water's, which has a pH of 7?

Accepted Answer

A)    
B)    
C)    
D)    
E) 7 
A)    
B)    
C)    
D)    
E) 7

Question 18

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 19

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 20

Solve for x:   . Round to 3 decimal places.

Accepted Answer

A) 1.362 
B) -1.362 
C) 1.517 
D) 0.517 
E) no solution 
A) 1.362 
B) -1.362 
C) 1.517 
D) 0.517 
E) no solution

Solve the equation. 2^x = 7

Simplify the expression .

Condense the expression to the logarithm of a single term.

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.

Graph the function using translations.

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

Find the graph of the function.

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.

Condense the expression to the logarithm of a single term.

Rewrite the logarithmic equation in exponential form.

Graph the function using translations.

An initial investment of $1000 grows at an annual interest rate of 7% compounded continuously. How long will it take to double the investment?

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.

Graph the function.

Simplify the expression.

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.2, how many times higher is its than pure water's, which has a pH of 7?

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

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

Solve for x: . Round to 3 decimal places.

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

Solve the equation. 2x = 7

Simplify the expression .

Condense the expression to the logarithm of a single term.

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.

Graph the function using translations.

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

Find the graph of the function.

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.

Condense the expression to the logarithm of a single term.

Rewrite the logarithmic equation in exponential form.

Graph the function using translations.

An initial investment of $1000 grows at an annual interest rate of 7% compounded continuously. How long will it take to double the investment?

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.

Graph the function.

Simplify the expression.

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.2, how many times higher is its than pure water's, which has a pH of 7?

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

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

Solve for x: . Round to 3 decimal places.

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

Solve the equation. 2^x = 7

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 below.