Multiple Choice. Identify the choice that best completes the statement or answers the question. 1. Evaluate the function at the indicated value of x. ...

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Review Sheet - 3.1-3.3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Evaluate the function at the indicated value of

3. Use a graphing utility to construct a table of

values for the function. Round your answer to two decimal places.

x . Round your result to three decimal places.

Function f (x ) 0.5 x a. b. c. d. e.

Value x 1.7

f (x ) 6 x

0.308 1.7 0.308 0.5 1.7

a.

b.

2. Match the graph with its exponential function. c.

d.

e.

x

2

1

0

1

2

f (x )

36

6

1

0.17

0.03

x

2

1

0

1

2

f (x )

36

6

1

0.17

0.03

x

2

1

0

1

2

f (x )

36

6

1

0.17

0.03

x

2

1

0

1

2

f (x )

36

6

1

0.17

0.03

x

2

1

0

1

2

f (x )

36

6

1

0.17

0.03

4. Use the graph of f to determine the

transformation that yields the graph of g . a. b. c. d. e.

f (x ) 3 x , g (x ) 3 x 8

x

y 2 3 y 2 x 3 y 2x 3 y 2x 3 y 2 x 3

a. b. c. d. e.

Shift the graph of f eight units to the left. Shift the graph of f eight units upward. Shift the graph of f eight units to the right. Shift the graph of f eight units downward. Both the graphs f and g are same.

5. Select the graph of the exponential function.

f (x ) 5 x 2 3

1

Name: ________________________

ID: A

a.

d.

b.

e.

c.

6. Use the One-to-One Property to solve the

equation for x . 4 x 1 1024 a. b. c. d. e.

2

x x x x x

8 4 7 5 6

Name: ________________________

ID: A

7. Use the One-to-One Property to solve the

11. Write the logarithmic equation in exponential

equation for x .

form.

ÊÁ 1 ˆ˜ x ÁÁÁ ˜˜˜ ÁÁÁ 2 ˜˜˜ 16 Ë ¯

log32 16

a. b. c. d. e.

x x x x x

4

5 4 4 5 6

a.

32 4

b.

32

c.

16

4

4

8. Evaluate the function f(x) 1.3 at x 3.6 . x

d.

Round to 3 decimal places. a. 1.690 b. 2.572 c. 5.287 d. 20.055 e. 4.680

32 4

e.

32

5

5

4 5

16 1 16

5

32

5

16 1 16

5

12. Write the exponential equation in logarithmic

form.

9. Use the One-to-One Property to solve the

4 2

following equation for x.

1 16

2 128 3x

a. b. c. d. e.

7 3 3 7 128 3 2 64 3

log16

b.

log4

c. d. e.

1 4 1

2

2 16 log4 16 2 1 log4 2 16 log4 16 2

13. Evaluate f (x ) logx at the indicated value of

10. Write the logarithmic equation in exponential

form.

x. Round your result to three decimal places.

log7 343 3 a. b. c. d. e.

a.

x 12.5 a. b. c. d. e.

7 343 2 7 3 77 7 3 343 7 3 14 343 7 2

3

–1.097 1.097 0.912 0.08 –0.912

Name: ________________________

ID: A

14. Evaluate the function at the indicated value of

17. Use the properties of logarithms to simplify the

x 32 .

expression.

f (x ) log2 x a. b. c. d. e.

9

0

log 9 24

1

a. b.

5

c.

1

d.

5 5 5

e.

15. Evaluate the function at the indicated value of

f (x ) log(x 4)

f (x ) log3 x

a.

b. c. d. e.

1 3

1

3 3 0 3

16. Evaluate the function at the indicated value of

x b 8 . g (x ) logb x b. a. b. c. d. e.

24

18. Select the graph of the function.

x 1.

a.

24 0 1 24 24 1

8 0 1 8 8 1 8

4

Name: ________________________

ID: A 19. Use the One-to-One Property to solve the

c.

equation for x. log2 (x 4 ) log2 20 a. b. c. d. e.

19 17 18 16 20

20. Use the One-to-One Property to solve the

equation for x. log2 (8x 2) log2 14

d.

a. b. c. d. e.

8 1 6 3 2 1 14 1 8

21. Rewrite the logarithm as a ratio of common

logarithms. e.

log5 17 a. b. c. d. e.

5

log5 log17 17 log 5 log17 log5 5 log 17 None of these

Name: ________________________

ID: A

22. Rewrite the logarithm as a ratio of common

25. Use the properties of logarithms to expand the

logarithms.

expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)

log3.1 x a. b. c. d. e.

log 3.1

log7

log x log x

a. b.

log 3.1 x log 3.1 log3.1x None of these

c. d. e.

23. Find the exact value of the logarithmic

expression without using a calculator.

2

2 3

y z

2 log7 x 2 log7 y 3 log7 z 2 log7 x 2 log7 y 3 log7 z 2 log7 x

2 log7 y 3 log7 z 2 log7 x 2 log7 y 3 log7 z 2 log7 x 2 log7 y 3 log7 z

26. Condense the expression to the logarithm of a

single quantity.

log6 36 a. b. c. d. e.

x

1È ÍÍ log (x 8 ) 2 log (x 8 ) ˙˘˙ 16 log x ˙˚ ÍÎ 7 7 7 2

2 6 36 6 None of these

a.

log7

24. Use the properties of logarithms to expand the

expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) log3 9x a. b. c. d. e.

b.

log7

c.

log7

d.

log3 9 log3 x log3 9 log3 x log3 9 log3 x log3 9 log3 x None of these

e.

6

log7 log7

(x 8 ) x 8 16

x

x x8

8

(x 8 ) (x 8 ) x 8 8

x

16

x x8

(x 8 ) x

16

x8

(x 8 )

Name: ________________________

ID: A 31. Find the exact value of log4 36 log4 9 without

27. Evaluate the logarithm using the

change-of-base formula. Round your result to three decimal places.

using a calculator. a. 1 b. 4 c. 9 9 d. 2 1 e. 2

log4 9 a. b. c. d. e.

1.585 5.585 3.585 4.585 2.585

32. Condense the expression log3 x log3 4 to the

logarithm of a single term. x a. log3 4 b. log3 4x

28. Use the properties of logarithms to rewrite and

simplify the logarithmic expression. Ê 4 8ˆ log2 ÁÁÁ 4 7 ˜˜˜ Ë ¯ a. b. c. d. e.

4 9 log2 8 9 4 log2 8 4 4 log2 7 8 8 log2 7 4 8 log2 7

29. Find the exact value of log8

3

64 without using

a calculator. 3 a. 64 16 b. 3 2 c. 3 d. –1 64 e. 3 ÊÁ 1 ˆ˜ 4 ˜˜ ÁË 27 ˜˜¯ .

30. Simplify the expression log3 ÁÁÁÁ a. b. c. d. e.

4 The expression cannot be simplified. –12 –108 1

7

4

c.

log3 x

d. e.

log(4x ) 3 log3 (x 4 )

ID: A

Review Sheet - 3.1-3.3 Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.

ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: OBJ: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: OBJ: ANS: ANS: OBJ: ANS: OBJ:

C PTS: 1 REF: 3.1.7 C PTS: 1 REF: 3.1.14 E PTS: 1 REF: 3.1.19a B PTS: 1 REF: 3.1.23 A PTS: 1 REF: 3.1.31 B PTS: 1 REF: 3.1.51 B PTS: 1 REF: 3.1.53 B PTS: 1 REF: 3.1.7 OBJ: Raise number to a non-integer power A PTS: 1 REF: 3.1.52 Solve exponential equations using one-on-one property C PTS: 1 REF: 3.2.8 D PTS: 1 REF: 3.2.11 D PTS: 1 REF: 3.2.19 B PTS: 1 REF: 3.2.31 E PTS: 1 REF: 3.2.23 D PTS: 1 REF: 3.2.25 D PTS: 1 REF: 3.2.28 A PTS: 1 REF: 3.2.36 B PTS: 1 REF: 3.2.79 D PTS: 1 REF: 3.2.85 C PTS: 1 REF: 3.2.88 C PTS: 1 REF: 3.3.7a B PTS: 1 REF: 3.3.13a A PTS: 1 REF: 3.3.29 C PTS: 1 REF: 3.3.46 D PTS: 1 REF: 3.3.63 A PTS: 1 REF: 3.3.84 A PTS: 1 REF: 3.3.15 D PTS: 1 REF: 3.3.24 C PTS: 1 REF: 3.3.32 Evaluate logarithmic function using properties of logarithms C PTS: 1 REF: 3.3.26 OBJ: Simplify logarithmic functions A PTS: 1 REF: 3.3.43 Evaluate logarithmic function using properties of logarithms B PTS: 1 REF: 3.3.71 Condense logarithmic function using the properties of logs

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