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# Exponents and Logarithms Practice Test

based on 7 ratings
By — McGraw-Hill Professional
Updated on Sep 2, 2011

Review the following concepts if needed:

## Exponents and Logarithms Practice Test

1. If \$ 10,000 is invested earning 6% annual interest, compounded quarterly, what will it be worth after eight years?

(a) \$15,938.48

(b) \$16,103.24

(c) \$11,264.93

(d) \$10,613.64

2. What is the present value of \$50,000 due in 10 years, earning 8% annual interest, compounded annually?

(a) \$107,946.25

(b) \$19,277.16

(c) \$23,159.67

(d) \$27,013.44

3. Rewrite log a x = w as an exponential equation.

(a) a w = x

(b) a x = w

(c) x a = w

(d) w a = x

4. Rewrite 7 m = n as a logarithmic equation.

(a) log n 7 = m

(b) log 7 m = n

(c) log m 7 = n

(d) log 7 n = m

5. e ln7 =

(a) ln 7

(b) 7

(c) e 7

(d) (ln 7) e

6. Rewrite as a single logarithm.

ln x − 2 ln y + ln z

7. Expand the logarithm.

8. Solve for x : log 6 ( x − 1) = 2.

(a) x = 3

(b) x = 37

(c) x = 13

(d) x = 65

9. Solve for x : log 4 ( x + 1) + log 4 ( x − 1) = log 4 8.

(a) x = 4

(b) x = ±3

(c) x = 3

(d) No solution

10. What is the domain for f ( x ) = log( x + 4)?

(a) (−∞, −4) ∪ (−4, ∞)

(b) (−∞, −4)

(c) (−4,∞)

(d) [−4,∞)

11. 11. Solve for x : 3 x +1 = 15.

(c) x = 4

(d) No solution

12. How long will it take for an investment to double if it earns 10% annual interest, compounded quarterly?

13. The half-life of a substance is about 40 years. What is its annual decay rate?

#### Solutions

1. B
2. C
3. A
4. D
5. B
6. A
7. D
8. B
9. C
10. B
11. B
12. D
13. C

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