Ch. 9 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Solve the given equation.
____
1.
a.
c.
7
9
b.
5
n=
3
8
9
d. n = 7
n=
n=
Evaluate the logarithmic expression.
____
2.
a.
b. 32,768
____
3. Solve
c.
d.
.
a.
4
3
b. 32
3
c. 8
d. 16
Solve the given equation. If necessary, round to four decimal places.
____
4.
a. 26
b. 1.4444
c. 0.69
d. 4
Solve the given equation. Round to the nearest ten-thousandth, if necessary.
____
5.
a. 1.4
b. 0.6592
c. 0.5666
d. 0.1682
Short Answer
Every ten years, the Bureau of the Census counts the number of people living in the United States. In 1830,
the population of the U.S. was 12.87 million. By 1840, this number had grown to 17.07 million.
6. Write the equation in terms of x, the number of decades x since 1830. Estimate the U.S. population in 2020 if
the population increases at the same rate.
Solve each equation.
7.
8. The 1965 Tacoma earthquake in Washington had a Richter scale magnitude of 6.5. Suppose an architect has
designed a building strong enough to withstand an earthquake 90 times as intense as the Tacoma quake. Find
the magnitude of the strongest quake this building can withstand.
Ch. 9 Review
Answer Section
MULTIPLE CHOICE
1. ANS: A
Eliminate the bases and use the Property of Equality for Exponential Functions to solve the equation.
Feedback
A
B
C
D
Correct!
Did you check the exponent of the base on the right side of the equation?
Did you write the right side of the equation in the correct exponential form?
Did you check the exponent of the base on the left side of the equation?
PTS: 1
DIF: Average
REF: Lesson 9-1
OBJ: 9-1.2 Solve exponential equations.
STA: {Key}12.0
TOP: Solve exponential equations.
KEY: Solve Equations | Exponential Equations
MSC: Key
2. ANS: D
Use the Property of Equality for Exponential Functions to evaluate the logarithmic expression.
Feedback
A
B
C
D
Use the Property of Equality for Exponential Functions.
Write the correct exponential form of the given expression.
The exponential and logarithmic functions are inverses.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 9-2
OBJ: 9-2.1 Evaluate logarithmic expressions.
STA: {Key}11.1 | {Key}11.2
TOP: Evaluate logarithmic expressions.
KEY: Logarithms | Evaluate Expressions | Logarithmic Expressions
MSC: Key
3. ANS: D
Use the definition of logarithms with base b to solve the logarithmic equation.
Feedback
A
B
C
D
Did you apply the definition of logarithm?
Did you simplify correctly?
What is the value on the right side of the equation?
Correct!
PTS: 1
DIF: Basic
REF: Lesson 9-2
OBJ: 9-2.2 Solve logarithmic equations.
STA: {Key}11.1 | {Key}11.2
TOP: Solve logarithmic equations.
KEY: Solve Equations | Logarithmic Equations
MSC: Key
4. ANS: B
Use the Product Property and the definition of logarithm.
Feedback
A
Did you substitute the values correctly?
B
C
D
Correct!
Have you used the Quotient Property of Logarithms?
Did you use the properties of logarithms?
PTS: 1
DIF: Average
REF: Lesson 9-3
OBJ: 9-3.2 Solve logarithmic equations using the properties of logarithms.
STA: {Key}11.0 | 14.0
TOP: Solve logarithmic equations.
KEY: Solve Equations | Logarithmic Equations
MSC: Key
5. ANS: D
Use natural logarithms to solve the equation.
Feedback
A
B
C
D
PTS:
OBJ:
STA:
KEY:
MSC:
Apply the Inverse Property of Exponents and Logarithms.
Did you verify the solution in the original equation?
Did you check the constant in the original equation?
Correct!
1
DIF: Average
REF: Lesson 9-5
9-5.2 Solve exponential equations using natural logarithms.
{Key}11.1
TOP: Solve exponential equations using natural logarithms.
Solve Equations | Exponential Equations | Natural Logarithms
Key
SHORT ANSWER
6. ANS:
2902.42 million
Use the formula
where y is the final population, is the initial population, b is the rate of increase
in the population, and x is the number of years. Replace the variables in the formula with the given values and
solve.
PTS: 1
STA: {Key}12.0
MSC: Key
7. ANS:
DIF: Advanced
REF: Lesson 9-1
TOP: Solve multi-step problems.
OBJ: 9-1.4 Solve multi-step problems.
KEY: Multi-step | Problem Solving
Use the Product Property and the Property of Equality for Logarithmic Functions.
PTS: 1
DIF: Advanced
STA: {Key}11.0 | 14.0
KEY: Multi-step | Problem Solving
8. ANS:
8.5
REF: Lesson 9-3
OBJ: 9-3.3 Solve multi-step problems.
TOP: Solve multi-step problems.
MSC: Key
Use the formula
PTS: 1
STA: 13.0
MSC: Key
, where M is the magnitude and I is the intensity.
DIF: Average
REF: Lesson 9-4
TOP: Solve multi-step problems.
OBJ: 9-4.4 Solve multi-step problems.
KEY: Multi-step | Problem Solving