Name: ______________________ Class: _________________ Date: _________
Ch. 3 - Exponential and Logarithmic Functions Quiz Review
____
1. Match the graph with its exponential function.
-x
a.
y=2
-3
b.
y = -2 + 3
c.
y=2 +3
d.
y=2 -3
e.
y = -2 - 3
x
x
x
x
1
ID: A
Name: ______________________
____
ID: A
2. Select the graph of the function.
f (x) = 5
x-1
a.
d.
b.
e.
c.
2
Name: ______________________
____
ID: A
3. Select the graph of the function.
f (x) = 6e
x+7
a.
d.
b.
e.
c.
3
Name: ______________________
____
ID: A
4. Write the logarithmic equation in exponential form.
log8 64 = 2
8
____
a. 64 = 2
2
b. 8 = 16
2
c. 8 = 88
2
d. 8 = 64
64
e. 8 = 2
5. Write the exponential equation in logarithmic form.
2
27 = 729
____
a.
log27 729 = 2
b.
log27 729 =
1
c.
2
log729 27 = 2
d.
log27 729 = -2
e.
log27 2 = 729
6. Use the properties of logarithms to simplify the expression.
log20 20
a.
0
b.
-
c.
d.
e.
9
1
9
1
9
-9
9
4
Name: ______________________
____
7. Use the properties of logarithms to simplify the expression.
log 9 24
9
a.
b.
24
0
c.
-
d.
e.
____
ID: A
1
24
-24
1
24
8. Write the logarithmic equation in exponential form.
ln (257) = 5.549. . .
____
5.549. . .
e
= -257
5.549. . .
e
= 257
-5.549. . .
e
= -257
1
5.549. . .
d. e
=
257
-5.549. . .
e. e
= 257
9. Write the exponential equation in logarithmic form.
a.
b.
c.
7
e = 1096.633. . .
a.
b.
c.
d.
e.
ln 1096.633. . . = -7
1
ln 1096.633. . . = 7
ln 1096.633. . . = 7
1
ln 1096.633. . . =
7
ln 7 = 1096.633. . .
5
Name: ______________________
____
ID: A
10. Select the graph of the function.
f (x) = log(x + 4)
a.
d.
b.
e.
c.
6
Name: ______________________
____
ID: A
11. Select the graph of the function.
f (x) = ln(x + 9)
a.
d.
b.
e.
c.
7
Name: ______________________
____
ID: A
12. Rewrite the logarithm as a ratio of common logarithms.
log5 17
a.
b.
c.
____
log5
log17
17
log
5
log17
log5
5
d. log
17
e. None of these
13. Use the properties of logarithms to expand the expression as a sum, difference, and/or constant
multiple of logarithms. (Assume all variables are positive.)
4
log2x y
a.
b.
c.
d.
e.
log2 ¥ 4 logx ¥ logy
log2 + 4 logx - logy
log2 + logx + 4 logy
log2 + 4 logx + logy
log2
4 ÊÁË logx + logy ˆ˜¯
8
Name: ______________________
____
14. Condense the expression to the logarithm of a single quantity.
ÍÈÍÍ ln (x + 6) + ln (x - 6) ˙˘˙˙
ÍÎ
˙˚
ln x -
____
ID: A
a.
ln
b.
ln
c.
ln
d.
ln
e.
ln
(x - 6)
x (x + 6)
(x + 6)
x (x - 6)
x (x - 6)
(x + 6)
x
(x - 6) (x + 6)
x (x + 6)
(x - 6)
15. Solve the exponential equation algebraically. Approximate the result to three decimal places.
e
5x
a.
b.
c.
d.
e.
=e
2
x - 14
-7, - 2
7, - 2
5, - 14
7, 2
-7, 2
9
Name: ______________________
____
ID: A
16. Solve the exponential equation algebraically. Approximate the result to three decimal places.
Ê xˆ
2 ÁÁÁÁ 3 ˜˜˜˜ = 36
Ë ¯
a.
b.
c.
d.
ln 18
ln 18
ln 3
ln 18
ln 3
ln 18
ln 3
ln 18
ª 2.631
ª -0.38
ª -2.631
ª 2.631
ª 0.38
ln 3
17. Solve the exponential equation algebraically. Approximate the result to three decimal places.
e.
____
ln 3
x
e - 8 = 12
a.
b.
c.
d.
e.
ln 20
ln 20
ln 20
ln 20
ln 20
ª
ª
ª
ª
ª
2.485
2.996
-2.485
2.079
-2.996
10
Name: ______________________
____
ID: A
18. Solve the exponential equation algebraically. Approximate the result to three decimal places.
Ê 4-x ˆ
4 ÁÁÁÁ 3 ˜˜˜˜ = 16
Ë
¯
a.
4-
b.
4-
c.
4-
d.
4-
____
ln 3
ln 4
ln 3
ln 4
ln 3
ln 4
ln 3
ln 4
ª 5.738
ª 6.738
ª 3.738
ª 4.738
ª 2.738
ln 3
19. Solve the logarithmic equation algebraically. Approximate the result to three decimal places.
e.
4-
ln 4
15 + 2 ln x = 2
a.
b.
c.
d.
e.
e
e
e
e
e
- 13 2
- 13 2
- 13 2
- 13 2
- 13 2
ª -1.998
ª 1.002
ª 2.002
ª 0.002
ª -0.998
11
Name: ______________________
____
ID: A
20. Solve the logarithmic equation algebraically. Approximate the result to three decimal places.
6 log3 (0.5x) = 5
a.
b.
c.
d.
e.
ÊÁ 5
2 ÁÁÁÁ 3
Ë
ÊÁ 5
2 ÁÁÁÁ 3
Ë
ÊÁ 5
2 ÁÁÁÁ 3
Ë
ÁÊ 5
2 ÁÁÁÁ 3
Ë
ÊÁ 5
2 ÁÁÁÁ 3
Ë
ˆ˜˜
˜˜˜
¯
6 ˆ
˜˜˜
˜˜
¯
6 ˆ
˜˜˜
˜˜
¯
ˆ˜
6 ˜
˜˜˜
¯
6 ˆ
˜˜˜
˜˜
¯
6
ª 3.996
ª 6.996
ª 4.996
ª 5.996
ª 2.996
12
ID: A
Ch. 3 - Exponential and Logarithmic Functions Quiz Review
Answer Section
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C
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1
3.1.14
3.1.21b
3.1.41b
3.2.7
3.2.16
3.2.33
3.2.36
3.2.55
3.2.59
3.2.79
3.2.82
3.3.7a
3.3.54
3.3.79
3.4.29
3.4.33
3.4.37
3.4.50
3.4.93
3.4.97