Algebra 2
NAME _____________________________
Chapter 7 Review for Final – Exponential and Logarithmic Functions
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 3 81 = 4
log 2 32
A.
A.
B.
B.
C.
C.
D.
D.
E.
E.
2. Rewrite the equation in logarithmic form.
4. Use the change-of-base formula to evaluate
the expression.
53 = 125
log 7 185
A.
A.
B.
B.
C.
C.
D.
D.
E.
E.
5. Match the function with its graph.
6. Match the function with its graph.
𝒇(𝒙) = 𝟑𝒙
𝒇(𝒙) = 𝒍𝒐𝒈𝟑 𝒙
2
D.
10. Condense the expression.
7. Expand the expression.
log 6 + log 5
ln 4𝑥
A.
A.
B.
B.
C.
C.
D.
D.
E.
E.
8. Expand the expression.
11. Condense the expression.
ln 9 − ln 𝑦
𝑥
log
5
A.
A.
B.
B.
C.
C.
D.
D.
E.
E.
12. Condense the expression.
9. Expand the expression.
3 log 𝑥 + log 8
3𝑥 2
log
7
A.
B.
A.
C.
B.
D.
C.
3
E.
E.
13. Solve the exponential equation.
16. Solve the logarithmic equation.
53𝑥 = 5𝑥+8
log 2 (2𝑥 + 5) = log 2 11
A.
A.
B.
B.
C.
C.
D.
D.
E.
E.
14. Solve the exponential equation.
17. Solve the logarithmic equation.
6
4𝑥−1
=6
𝑥+5
log 3 (5𝑥) = log 3 40
A.
A.
B.
B.
C.
C.
D.
D.
E.
E.
18. Solve the logarithmic equation.
15. Solve the exponential equation.
33𝑥−1 = 9𝑥+2
log(7𝑥 + 4) = log(2𝑥 − 16)
A.
A.
B.
B.
C.
C.
D.
D.
4
E.
21. Solve the exponential equation.
19. Solve the exponential equation.
𝑒𝑥 = 2
4𝑥 = 60
A.
A.
B.
B.
C.
C.
D.
D.
E.
E.
22. Solve the logarithmic equation.
20. Solve the logarithmic equation.
ln (2𝑥 + 7) = 3
log 3 𝑥 = 3
A.
A.
B.
B.
C.
C.
D.
D.
E.
E.
5
23. You deposit $5000 in an account that earns
2.5% annual interest. Find the balance after 3
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 45,000,000
kilowatt-hours of energy.
What is the earthquake’s magnitude?
A.
B.
C.
D.
A.
E.
B.
C.
24. You buy a new car for $25,000. The value
of the car decreases by 18% each year. What is
the value of the car after four years?
D.
E.
𝒚 = 𝒂(𝟏 − 𝒓)𝒕
A.
B.
C.
D.
E.
6