Name: _____________________________________ Period: __________ Date: ______________ID: A
Algebra II Chapter 8 Practice Test
1. Write an exponential function y = ab x for a graph
that includes (0, 3.5) and (1, 17.5).
11. State the property or properties of logarithms used
to rewrite the expression.
1
20
log 625x 4 = log 5x
5
ÊÁ 1 ˆ˜ x
2. Graph y = − 2ÁÁÁÁ ˜˜˜˜ .
Ë 7¯
12. Write the expression as a single logarithm.
log 3 4 − log 3 2
Determine whether the function represents
exponential decay or exponential growth.
Identify the horizontal asymptote.
13. Expand the logarithmic expression.
x
3. Graph f(x) = e + 3 .
Identify the horizontal asymptote.
log b
4. State the property or properties of logarithms used
to rewrite the expression.
1
2 log 6 + log = log 12
3
57
74
14. Use the properties of logarithms to evaluate
log 3 9 + log3 36 − log 3 4 .
15. Solve 15 2x = 36. Round to the nearest
ten-thousandth.
5. Evaluate the logarithm. log 3 243
16. Use the Change of Base Formula to evaluate
log 4 20 . Then convert log 4 20 to a logarithm in base
3. Round to the nearest thousandth.
6. Suppose you invest $1500 at an annual interest rate
of 3.7% compounded continuously. How much will
you have in the account after 10 years?
17. Solve 125 9x − 2 = 150.
7. Evalute log 8 256 + log 8 16 as a single logarithm.
18. Solve 3 log 2x = 4. Round to the nearest
ten-thousandth.
8. Write the expression as a single logarithm.
5 log b q + 2 logb y
19. Solve log(x + 9) − log x = 3 . Round to the nearest
ten-thousandth.
9. Write the equation in logarithmic
4
form.125 3 = 625
10. Write the equation log 32 8 =
20. Solve 2 log 4 − log 3 + 2 log x − 4 = 0. Round to
the nearest ten-thousandth.
3
in exponential form.
5
21. Write the expression as a single natural logarithm.
3 ln 3 + 3 lnc
1
ID: A
22. Write the expression as a single natural logarithm.
1
3 ln a − (ln b + ln c 2 )
2
30. Graph y = 7 (6)
x+2
+ 1.
31. Write an exponential function y = ab x for a graph
that includes (1, 15) and (0, 6).
23. Simplify ln e 3 .
32. Graph the function. Identify the horizontal
asymptote.
ÊÁ 1 ˆ˜ x − 1
+ 1.
Graph y = 2ÁÁÁÁ ˜˜˜˜
Ë 5¯
24. Solve ln 2 + ln x = 5 . Round to the nearest
thousandth, if necessary.
25. Solve ln x − ln 6 = 0 .
33. Use a graphing calculator. Use the graph of y = e x
to evaluate e 1.7 to four decimal places.
26. Use natural logarithms to solve the equation. Round
to the nearest thousandth.
6e 4x − 2 = 3
34. Write the equation in logarithmic form.
6 4 = 1, 296
27. Use natural logarithms to solve the equation. Round
to the nearest thousandth.
e 2x = 1.4
35. Solve
1
= 644x − 3 .
16
28. Write an exponential function for the graph.
36. Use the Change of Base Formula to solve 2 2x = 90.
Round to the nearest ten-thousandth.
37. Solve ln(2x − 1) = 8 . Round to the nearest
thousandth.
29. The amount of money in an account with
continuously compounded interest is given by the
formula A = Pe rt , where P is the principal, r is the
annual interest rate, and t is the time in years.
Calculate to the nearest hundredth of a year how
long it takes for an amount of money to double if
interest is compounded continuously at 6.2%.
Round to the nearest tenth.
2
ID: A
Algebra II Chapter 8 Practice Test
Answer Section
1. ANS:
y = 3.5(5) x
TOP: 8-1 Example 3
2. ANS:
TOP: 8-2 Example 1
3. ANS:
TOP: 7-6 The Natural Base e
4. ANS:
Power Property and Product Property
TOP: 8-4 Example 1
5. ANS:
5
TOP: 8-3 Example 3
1
ID: A
6. ANS:
$2,171.60
TOP: 8-2 Example 5
7. ANS:
4
TOP: 7-4 Properties of Logarithms
8. ANS:
log b (q 5 y 2 )
TOP: 8-4 Example 2
9. ANS:
4
log 125 625 =
3
TOP: 8-3 Example 2
10. ANS:
3
32 5 = 8
TOP: 8-3 Example 3
11. ANS:
Power Property
TOP: 8-4 Example 1
12. ANS:
log 3 2
TOP: 8-4 Example 2
13. ANS:
1
1
logb 57 − log b 74
2
2
14. ANS:
4
TOP: 8-4 Example 5
15. ANS:
0.6616
TOP: 8-5 Example 1
16. ANS:
2.161; log 3 10.741
TOP: 8-5 Example 5
2
ID: A
17. ANS:
0.3375
TOP: 8-5 Example 5
18. ANS:
10.7722
TOP: 8-5 Example 6
19. ANS:
0.0090
TOP: 8-5 Example 7
20. ANS:
43.3013
TOP: 8-5 Example 7
21. ANS:
ln 27c 3
TOP: 8-6 Example 1
22. ANS:
a3
ln
c b
TOP: 8-6 Example 1
23. ANS:
3
TOP: 8-6 Example 1
24. ANS:
74.2
TOP: 8-6 Example 3
25. ANS:
6
26. ANS:
–0.046
TOP: 8-6 Example 4
27. ANS:
0.168
TOP: 8-6 Example 4
28. ANS:
y = 0.5(2) x
TOP: 8-1 Example 3
3
ID: A
29. ANS:
11.2 yr
TOP: 8-6 Example 5
30. ANS:
TOP: 8-2 Example 2
31. ANS:
y = 6(2.5) x
TOP: 8-1 Example 3
32. ANS:
TOP: 8-2 Example 2
33. ANS:
5.4739
TOP: 8-2 Example 4
4
ID: A
34. ANS:
log 6 1, 296 = 4
TOP: 8-3 Example 2
35. ANS:
7
12
TOP: 8-5 Example 5
36. ANS:
3.2459
TOP: 8-5 Example 5
37. ANS:
1,490.979
TOP: 8-6 Example 3
5