Chapter 3 Final Review - Exponential and Logarithmic Functions
Indicate the answer choice that best completes the statement or answers the question.
1. FINANCIAL LITERACY If $500 is deposited in a savings account providing an annual interest rate of 5.6%
compounded quarterly, how long will it take for the account to be worth $750?
a. –7.29 years
b. 7.29 years
c. 1 years
d. 6.50 years
Solve each equation. Round to the nearest hundredth.
2. 3x – 8 + 2 = 38
a. 44
b. 11.26
c. –11.26
d. 0.02
Solve each equation.
3. 3e4x – 9e2x – 15 = 0
a.
b. –0.7167
c. 0.7167
d. no solution
Expand each expression.
4. log2 [(2x)3(x + 1)]
a. 3 + 3 log2 x log2 (x + 1)
b. 3 + 3 log2 (2x + 1)
c. 3 + 2 log3 x + log2 (x + 1)
d. 3 + 3 log2 x + log2 (x + 1)
Solve each equation.
5. log5 (x + 4) + log5 x = log5 12
a. 2
b. –2
c. 0
d. no solution
6. 6 ln (x + 2) – 3 = 21
a. no solution
b. 22
c. –52.6
d. 52.6
Chapter 3 Final Review - Exponential and Logarithmic Functions
Express each logarithm in terms of ln 10 and ln 3.
7. ln 300
a. ln 3 + 10 ln 2
b. ln 3 + 2 ln 10
c. ln 3 + ln 100
d. ln 3 2 ln 10
Solve each equation.
8. 2–4x + 1 = 32x – 3
a.
b. 0.80
c. –0.80
d. no solution
9. ln 0.04x = –8
a.
b.
c. –200
d. no solution
10. BANKING Ms. Cubbatz invested a sum of money in a certificate of deposit that earns 8% interest compounded
continuously. The formula for calculating interest that is compounded continuously is A = Pert. If Ms. Cubbatz made the
investment on January 1, 2005, and the account was worth $12,000 on January 1, 2009, what was the original amount in
the account?
a. $–8713.79
b. $8713.79
c. $3286.21
d. $12,000
Solve each equation.
11. log (2x + 1) + log (x – 4) = log (2x2 – 4)
a. –3
b. 2 and –1
c. 4
d. no solution
Evaluate each logarithm.
12. log0.24 322
a. 4.046
b. –4.046
c. –519.532
d. –0.247
Chapter 3 Final Review - Exponential and Logarithmic Functions
Condense each expression.
13.
a.
b.
c.
d.
Solve each equation.
14.
a.
b.
c. 3
d. no solution
Solve each equation. Round to the nearest hundredth.
15. 43x = 1056
a. 1.67
b. 0.38
c. –1.67
d. 264
Evaluate each expression.
16. log10 0.001
a. 1
b. 0.01
c. –3
d. 3
Solve each equation.
17.
a. –1
b. 1
c. 0
d. no solution
Chapter 3 Final Review - Exponential and Logarithmic Functions
Express each logarithm in terms of ln 10 and ln 3.
18. ln 27000
a. 3 ln 3 + 3 ln 10
b. 3 ln 3 3 ln 10
c. 3 ln 3 + 10 ln 3
d. 3 ln 3 + ln 1000
Expand each expression.
19.
a.
b.
c.
d.
Express each logarithm in terms of ln 10 and ln 3.
20.
a. ln 729 – ln 10,000
b. 6 ln 3 4 ln 10
c. 6 ln 3 – 4 ln 10
d. 3 ln 6 – 10 ln 4
Solve each equation.
21. 4e2x – 13ex + 9 = 0
a. 0 and –0.811
b. 0
c. 3
d. 0 and 0.811
Expand each expression.
23.
a.
b.
c.
d.
Chapter 3 Final Review - Exponential and Logarithmic Functions
Sketch and analyze the graph of each function. Describe its domain, range, intercepts, asymptotes, end behavior,
and where the function is increasing or decreasing.
22. g(x) = e2x + 1
a. D = (– , ); R = (0,
b. D = (– ,
);
y-intercept: (0, e) or (0, 2.72); x-intercept: none;
asymptote: x-axis; end behavior:
; increasing: (– ,
c. D = (– ,
); R = (– ,
); R = (0,
);
y-intercept: (0, 0.3); x-intercept: none; asymptote:
and
x-axis; end behavior:
)
and
; increasing: (– ,
d. D = (– ,
);
); R = (0,
)
);
y-intercept: (0, 2); x-intercept: none; asymptote: x =
y-intercept: (0, e) or (0, 2.72); x-intercept: none;
1; end behavior:
asymptote: x-axis; end behavior:
increasing: (– ,
and
)
;
and
; decreasing: ( , – )
Chapter 3 Final Review - Exponential and Logarithmic Functions
Sketch and analyze the graph of each function. Describe its domain, range, intercepts, asymptotes, end behavior,
and where the function is increasing or decreasing.
24. f(x) = 3x
a. D = (– ,
); R = (0,
b. D = ( , – ); R = ( , 0);
);
y-intercept: 1; x-intercept: none;
asymptote: x-axis; end behavior:
;
increasing: (– ,
c. D = (– ,
y-intercept: 1; x-intercept: none;
and
asymptote: x-axis; end behavior:
and
)
); R = (– ,
;
decreasing: (– ,
);
d. D = (– ,
)
); R = (0,
);
y-intercept: 0; x-intercept: 0;
y-intercept: 0; x-intercept: 0;
asymptote: none; end behavior:
asymptote: y = –1; end behavior:
and
;
and
;
increasing: (– ,
)
increasing: (– ,
)
Chapter 3 Final Review - Exponential and Logarithmic Functions
25. Use the graph of f to describe the transformation that results in the graph of g. Then sketch the graphs of f and g.
f(x) = ln x,
a. The graph of g(x) is the graph of f(x) shifted 2
units
b. The graph of g(x) is the graph of f(x) reflected over the
x-axis.
up and compressed horizontally by a factor of
.
c. The graph of g(x) is the graph of f(x) shifted 2
units
down and compressed horizontally by a factor
of
.
d. The graph of g(x) is the graph of f(x) shifted 2 units
down and reflected over the y-axis.
Chapter 3 Final Review - Exponential and Logarithmic Functions
Sketch and analyze the graph of each function. Describe its domain, range, intercepts, asymptotes, end behavior,
and where the function is increasing or decreasing.
26. g(x) = 4–x + 2
a. D = (– , ); R = (0,
b. D = (– ,
);
); R = (0,
);
y-intercept: (0, 16); x-intercept: none; asymptote: x-
y-intercept: (0, 16); x-intercept: none; asymptote: x-
axis; end behavior:
axis; end behavior:
and
; increasing: (– ,
c. D = (– ,
); R = (0,
)
; decreasing: (– ,
d. D = (– ,
);
and
); R = (0,
)
);
y-intercept: (0, 0); x-intercept: none; asymptote: x-
y-intercept: (0, 3); x-intercept: none; asymptote: x-
axis; end behavior:
axis; end behavior:
; decreasing: (– ,
and
)
; decreasing: (– ,
and
)
Chapter 3 Final Review - Exponential and Logarithmic Functions
Sketch and analyze the graph of each function. Describe its domain, range, intercepts, asymptotes, end behavior,
and where the function is increasing or decreasing.
27.
a. D = (– ,
); R = (– , –2);
b. D = (– ,
); R = (– , 0);
y-intercept: (0, –1.8); x-intercept: 2.2;
y-intercept: (0, 0); x-intercept: none;
asymptote: y = –2; end behavior:
asymptote: y = 0; end behavior:
and
;
increasing: (– ,
)
c. D = (– ,
and
;
decreasing: (– ,
); R = (– , –2);
d. D = (– ,
)
); R = (– ,
);
y-intercept: (0, –2.2); x-intercept: none;
y-intercept: (0, 0.4); x-intercept: (2, 0);
asymptote: y = –2; end behavior:
asymptote: none; end behavior:
and
;
decreasing: (– ,
)
;
decreasing: (– ,
)
and
Chapter 3 Final Review - Exponential and Logarithmic Functions
Solve each equation.
28. ln (2x – 1) = ln 16
a.
b.
c. 8
d. no solution
Evaluate each expression.
29. log7 73
a. 3
b. 343
c. 7
d. 21
Solve each equation.
30. log6 x + log6 9 = log6 54
a. 45
b. –6
c. 6
d. no solution
31. 6e6x – 17e3x + 7 = 0
a. –0.28 and –1.5
b. –0.23
c. 0.28 and –0.23
d. no solution
Solve each equation. Round to the nearest hundredth.
32. 5x + 3 – 4 = 19
a. 3
b. 1.05
c. 2.11
d. –1.05
Solve each equation.
33. ln (x – 5) + ln 4 = ln x – ln 2
a.
b. 6
c. –8
d.
Chapter 3 Final Review - Exponential and Logarithmic Functions
Answer Key
1. b
2. b
3. c
4. d
5. a
6. d
7. b
8. b
9. b
10. b
11. d
12. b
13. d
14. a
15. a
16. c
17. a
18. a
19. a
20. c
21. d
22. b
23. a
24. a
25. c
26. b
27. c
Chapter 3 Final Review - Exponential and Logarithmic Functions
28. b
29. a
30. c
31. c
32. d
33. d