Deck 4: Exponential and Logarithmic Functions

Question 1

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Answer 1

Question 2

Rewrite the logarithm in terms of the natural logarithm.

A)
B)
C)
D)
E)

Answer 2

Question 3

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

A)2.468
B)2.921
C)11.060
D)5.684
E)0.342

Answer 3

2.921

Question 4

Find the exact value of without using a calculator.

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

Question 5

Let Q represent a mass of radioactive radium (²²⁶Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is Determine the quantity present after 200 years. Round to the nearest hundredth of a gram.

A)3.67 g
B)4.00 g
C)0.25 g
D)0.92 g
E)0.00 g

Question 6

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

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

Question 7

Write the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 8

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 9

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

A)2.061
B)4.745
C)3.061
D)3.561
E)2.561

Question 10

Evaluate the function at . Round to 3 decimal places.

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

Question 11

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

A)26.822
B)99.373
C)45.553
D)599.708
E)7.721

Question 12

Simplify the expression .

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

Question 13

Rewrite the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 14

Solve the equation for x using the One-to-One Property.

A)-9
B)-11
C)11
D)0
E)The equation has no solution.

Question 15

Rewrite the logarithmic equation in exponential form.

A)
B)
C)
D)
E)

Question 16

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

A)
B)
C)
D)
E)

Question 17

Evaluate the function at . Round to 3 decimal places. (You may use your calculator.)

A)-2.241
B)undefined
C)1.707
D)4.272
E)-1.707

Question 18

Simplify the expression .

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

Question 19

Identify the x-intercept of the function .

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

Question 20

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 21

Evaluate the function at . Round to 3 decimal places.

A)2.700
B)2.075
C)2.250
D)5.203
E)2.415

Question 22

Solve the equation for x using the One-to-One Property.

A)-1
B)-101
C)-99
D)The equation has no solution.
E)101

Question 23

Rewrite the logarithm in terms of the natural logarithm.

A)
B)
C)
D)
E)

Question 24

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 3.4, how many times higher is its than pure water's, which has a pH of 7?

A)
B)
C)7
D)
E)

Question 25

Evaluate the function at . Round to 3 decimal places. (You may use your calculator.)

A)2.079
B)-13.038
C)13.038
D)-6.125
E)undefined

Question 26

Rewrite the logarithmic equation in exponential form.

A)
B)
C)
D)
E)

Question 27

Solve for x: . Round to 3 decimal places.

A)0.663
B)1.362
C)3.663
D)-1.362
E)no solution

Question 28

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

A)
B)
C)
D)
E)2

Question 29

Simplify the expression .

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

Question 30

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

A)
B)
C)
D)
E)

Question 31

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

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

Question 32

Let Q represent a mass of radioactive radium (²²⁶Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is Determine the quantity present after 200 years. Round to the nearest hundredth of a gram.

A)0.00 g
B)4.00 g
C)0.92 g
D)3.67 g
E)0.25 g

Question 33

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

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

Question 34

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

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

Question 35

Write the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 36

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

A)0.402
B)2.485
C)9.411
D)4.836
E)2.100

Question 37

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

A)6.572
B)3.354
C)2.854
D)3.854
E)4.354

Question 38

Rewrite the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 39

Find the exact value of without using a calculator.

A)3
B)2
C)1.5
D)0.75
E)1

Question 40

Identify the x-intercept of the function .

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

Question 41

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

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

Question 42

Find the exact value of without using a calculator.

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

Question 43

Simplify the expression .

A)The expression cannot be simplified.
B)3
C)-6
D)1
E)-27

Question 44

Solve the equation for x using the One-to-One Property.

A)11
B)-9
C)-11
D)0
E)The equation has no solution.

Question 45

Solve for x: . Round to 3 decimal places.

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

Question 46

Rewrite the logarithmic equation in exponential form.

A)
B)
C)
D)
E)

Question 47

Write the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 48

Evaluate the function at . Round to 3 decimal places.

A)5.287
B)4.680
C)20.055
D)2.572
E)1.690

Question 49

Evaluate the function at . Round to 3 decimal places. (You may use your calculator.)

A)-2.928
B)3.391
C)-3.391
D)2.150
E)undefined

Question 50

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 51

Let Q represent a mass of radioactive radium (²²⁶Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is Determine the quantity present after 300 years. Round to the nearest hundredth of a gram.

A)0.00 g
B)0.47 g
C)0.88 g
D)4.39 g
E)5.00 g

Question 52

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 53

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 3.3, how many times higher is its than pure water's, which has a pH of 7?

A)
B)
C)
D)
E)7

Question 54

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

A)2
B)
C)
D)
E)

Question 55

Rewrite the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 56

An initial investment of $6000 grows at an annual interest rate of 7% compounded continuously. How long will it take to double the investment?

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

Question 57

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 58

Identify the x-intercept of the function .

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

Question 59

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

A)42.051
B)37.296
C)7.597
D)26.492
E)82.783

Question 60

Find the exact value of without using a calculator.

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

Question 61

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 62

Graph the exponential function.

A)
B)
C)
D)

Question 63

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

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

Question 64

Simplify the expression .

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

Question 65

Graph the function using translations.

A)
B)
C)
D)

Question 66

Rewrite the logarithm in terms of the natural logarithm.

A)
B)
C)
D)
E)

Question 67

Graph the function.

A)
B)
C)
D)

Question 68

Identify the graph of the function.

A)
B)
C)
D)
E)

Question 69

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

A)
B)
C)
D)
E)

Question 70

Find the exact value of without using a calculator.

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

Question 71

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

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

Question 72

Solve for x: . Round to 3 decimal places.

A)2.407
B)0.407
C)1.362
D)-1.362
E)no solution

Question 73

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 74

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

A)
B)
C)
D)
E)2

Question 75

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?

A)
B)
C)
D)
E)7

Question 76

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 77

An initial investment of $9000 grows at an annual interest rate of 5% compounded continuously. How long will it take to double the investment?

A)13.86 years
B)14.86 years
C)14.40 years
D)13.40 years
E)1 year

Question 78

Simplify the expression .

A)
B)
C)6
D)
E)The expression cannot be simplified.

Question 79

Find the exact value of without using a calculator.

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

Question 80

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

A)
B)
C)
D)
E)