Algebra 2
Chapter 7 Review for Final 2
NAME _____________________________
25 Minutes – 25 Questions
DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on
your answer document. Students may write on this test, and you can use your answer document as
scratch paper. Refer to the formula sheet when needed. You are permitted to use a calculator on this
test. Illustrative figures are NOT necessarily drawn to scale.
1. Rewrite the equation in exponential form.
3. Use the change-of-base formula to evaluate
the expression.
log 2 32 = 5
A. 25 = 16
5
B. 2 = 32
2
C. 32 = 5
2
log 3 27
A.
1
2
B. 1
C. 3
D. 5 = 32
D. 4
E. 232 = 5
E. 5
2. Rewrite the equation in logarithmic form.
43 = 64
4. Use the change-of-base formula to evaluate
the expression.
log 6 150
A. log 3 4 = 64
A. ≈ 0.333
B. log 3 64 = 4
B. ≈ 1.792
C. log 4 3 = 64
C. ≈ 2.796
D. log 64 2 = 4
D. ≈ 3.648
E. log 4 64 = 3
E. ≈ 4.876
5. Match the function with its graph.
6. Match the function with its graph.
𝒇(𝒙) = 𝟑𝒙
𝒇(𝒙) = 𝒍𝒐𝒈𝟑 𝒙
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7. Expand the expression.
10. Condense the expression.
log 7 + log 8
ln 5𝑥
A. log 15
A. ln 5 + ln 𝑥
7
8
B. log ( )
B. ln 5 − ln 𝑥
C. 5 ln 𝑥
C. 7 log 8
D. (ln 5) × (ln 𝑥)
D. log 56
E. 𝑥 ln 5
E. 7 log 8
8. Expand the expression.
11. Condense the expression.
ln 11 − ln 𝑦
𝑥
6
log
A. ln(11 − 𝑦)
𝑦
)
11
A. log 𝑥 + log 6
B. ln (
B. log 𝑥 − log 6
C. ln 11 𝑦
C. 𝑥 log 6
D. 11 ln 𝑦
D. log 6 − log 𝑥
E. 6 log 𝑥
E. ln (
11
)
𝑦
9. Expand the expression.
12. Condense the expression.
log
4𝑥
9
3
2 log 𝑥 + log 3
A. log 4 − (3 log 𝑥 + log 9)
A. log 2𝑥
B. 3 (log 4 + log 𝑥) − log 9
B. log 3𝑥
C. log 4 + 3 log 𝑥 − log 9
C. log 3𝑥 2
D. − log 4 − 3 log 𝑥 − log 9
D. log 2𝑥 3
3
13. Solve the exponential equation.
16. Solve the logarithmic equation.
72𝑥 = 7𝑥+8
log 20 (2𝑥 + 9) = log 20 13
A. 𝑥 = 1
A. 𝑥 = 1
B. 𝑥 = 2
B. 𝑥 = 2
C. 𝑥 = 3
C. 𝑥 = 3
D. 𝑥 = 4
D. 𝑥 = 4
E. 𝑥 = 8
E. 𝑥 = 5
14. Solve the exponential equation.
17. Solve the logarithmic equation.
25𝑥−1 = 2𝑥+3
log13 (6𝑥) = log13 48
A. 𝑥 = 5
A. 𝑥 = 1
B. 𝑥 = 6
B. 𝑥 = 2
C. 𝑥 = 7
C. 𝑥 = 3
D. 𝑥 = 8
D. 𝑥 = 4
E. 𝑥 = 9
E. 𝑥 = 5
18. Solve the logarithmic equation.
15. Solve the exponential equation.
25𝑥−3 = 8𝑥+1
ln(6𝑥 + 3) = ln(2𝑥 − 5)
A. 𝑥 = 1
A. 𝑥 = −4
B. 𝑥 = 2
B. 𝑥 = −3
C. 𝑥 = 3
C. 𝑥 = −2
D. 𝑥 = 4
D. 𝑥 = −1
E. 𝑥 = 5
E. 𝑥 = 0
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19. Solve the exponential equation.
21. Solve the exponential equation.
4𝑥 = 160
𝑒𝑥 = 4
A. ≈ 0.339
A. ≈ 0.693
B. ≈ 1.998
B. ≈ 1.386
C. ≈ 2.953
C. ≈ 2.337
D. ≈ 3.661
D. ≈ 3.084
E. ≈ 4.018
E. ≈ 4.018
22. Solve the logarithmic equation.
20. Solve the logarithmic equation.
ln (3𝑥 + 6) = 4
log 3 𝑥 = 4
A. ≈ 3.272
A. 𝑥 = 1
B. ≈ 4.695
B. 𝑥 = 3
C. ≈ 10.043
C. 𝑥 = 9
D. 𝑥 = 27
D. ≈ 16.199
E. 𝑥 = 81
E. ≈ 20.086
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23. You deposit $5000 in an account that earns
3.5% annual interest. Find the balance after 2
years if the interest is compounded monthly.
25. The Richter magnitude R is given by the
model:
𝑹 = 𝟎. 𝟔𝟕 ∙ 𝐥𝐨𝐠(𝟎. 𝟑𝟕𝑬) + 𝟏. 𝟒𝟔
𝒏𝒕
𝒓
𝑨 = 𝑷 (𝟏 + )
𝒏
Where E is the energy (in kilowatt-hours)
released by the earthquake.
Suppose an earthquake releases 850,000,000
kilowatt-hours of energy.
What is the earthquake’s magnitude?
A. ≈ $5126.44
B. ≈ $5256.08
C. ≈ $5361.99
D. ≈ $5665.01
A. ≈ 5.4
E. ≈ $10,503.75
B. ≈ 6.3
C. ≈ 7.2
24. You buy a new car for $25,000. The value
of the car decreases by 25% each year. What is
the value of the car after 3 years?
D. ≈ 8.1
E. ≈ 9.0
𝒚 = 𝒂(𝟏 − 𝒓)𝒕
A. ≈ $48,469
B. ≈ $20,500
C. ≈ $13,784
D. ≈ $10,547
E. ≈
$9,268
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