Question 1

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 2

Write the exponential equation   in logarithmic form.

Accepted Answer

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

Question 3

Write the exponential equation   in logarithmic form.

Accepted Answer

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

Question 4

Condense the expression   to the logarithm of a single term.

Accepted Answer

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

Question 5

Find the exact value of   without using a calculator.

Accepted Answer

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

Question 6

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

Accepted Answer

A) b = 3.7 
B) b = 4.3 
C) b = 1 
D) b = 4 
E) b = 3 
A) b = 3.7 
B) b = 4.3 
C) b = 1 
D) b = 4 
E) b = 3

Question 7

Simplify the expression.

Accepted Answer

A) 56 
B) 8 
C) 7 
D) 64 
E) none of these 
A) 56 
B) 8 
C) 7 
D) 64 
E) none of these

Question 8

Simplify the expression.

Accepted Answer

A) 2 
B) 4 
C) 18 
D) 9 
E) none of these 
A) 2 
B) 4 
C) 18 
D) 9 
E) none of these

Question 9

Simplify the expression   .

Accepted Answer

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

Question 10

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

Accepted Answer

A)    
B)    
C)    
D)    
E) 2 
A)    
B)    
C)    
D)    
E) 2

Question 11

Rewrite the logarithm   in terms of the natural logarithm.

Accepted Answer

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

Question 12

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 13

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

Accepted Answer

A) 0.630 
B) -0.692 
C) -1.745 
D) -0.573 
E) 0.273 
A) 0.630 
B) -0.692 
C) -1.745 
D) -0.573 
E) 0.273

Question 14

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 79 grams, how much will remain after 6 years?

Accepted Answer

A) 0.0725 grams 
B) 62.5417 grams 
C) 56.4895 grams 
D) 18.8581 grams 
E) 19.7500 grams 
A) 0.0725 grams 
B) 62.5417 grams 
C) 56.4895 grams 
D) 18.8581 grams 
E) 19.7500 grams

Question 15

Graph the function using translations.

Accepted Answer

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

Question 16

Find the graph of the function.

Accepted Answer

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

Question 17

Solve the equation. 2x = 5

Accepted Answer

A) x = 1.6652 
B) x = 0.4307 
C) x = 0.5541 
D) x = 5.8628 
E) x = 1.4307 
A) x = 1.6652 
B) x = 0.4307 
C) x = 0.5541 
D) x = 5.8628 
E) x = 1.4307

Question 18

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 69 grams, how much will remain after 75 years?

Accepted Answer

A) 0.0000 grams 
B) 61.5289 grams 
C) 1.5848 grams 
D) 17.2500 grams 
E) 1.0426 grams 
A) 0.0000 grams 
B) 61.5289 grams 
C) 1.5848 grams 
D) 17.2500 grams 
E) 1.0426 grams

Question 19

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

Accepted Answer

A) b = 3.5 
B) b = 2.5 
C) b = 4 
D) b = 3 
E) b = 2 
A) b = 3.5 
B) b = 2.5 
C) b = 4 
D) b = 3 
E) b = 2

Question 20

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

Accepted Answer

A) -0.154 
B) 0.323 
C) -0.355 
D) 3.093 
E) 0.390 
A) -0.154 
B) 0.323 
C) -0.355 
D) 3.093 
E) 0.390

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

Write the exponential equation in logarithmic form.

Write the exponential equation in logarithmic form.

Condense the expression to the logarithm of a single term.

Find the exact value of without using a calculator.

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

Simplify the expression.

Simplify the expression.

Simplify the expression .

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

Rewrite the logarithm in terms of the natural logarithm.

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

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

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 79 grams, how much will remain after 6 years?

Graph the function using translations.

Find the graph of the function.

Solve the equation. 2^x = 5

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 69 grams, how much will remain after 75 years?

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

Evaluate the logarithm using the change of base formula. 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

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

Write the exponential equation in logarithmic form.

Write the exponential equation in logarithmic form.

Condense the expression to the logarithm of a single term.

Find the exact value of without using a calculator.

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

Simplify the expression.

Simplify the expression.

Simplify the expression .

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

Rewrite the logarithm in terms of the natural logarithm.

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

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

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 79 grams, how much will remain after 6 years?

Graph the function using translations.

Find the graph of the function.

Solve the equation. 2x = 5

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 69 grams, how much will remain after 75 years?

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

Evaluate the logarithm using the change of base formula. 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

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

Solve the equation. 2^x = 5