Name: ________________________ Class: ___________________ Date: __________

ID: A

Exponentials and Logarithms Multiple Choice Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. ____

1. Which function is an example of exponential decay? Ê ˆx 0.9 C c (x )  5 (x ) A a (x )  0.5 ÁÁÁ 2 ˜˜˜ Ë ¯ ˆx ÊÁ ÁÁ 3 ˜˜˜ ˆ Ê ˜˜ B b (x )  2.4 ÁÁÁ D d (x )  ln ÁÁ x 0.9 ˜˜ ÁÁ 2 ˜˜˜ ¯ Ë ¯ Ë

____

2. The population of Whoville has been decreasing at a rate of 0.8% per year since Dr. Seuss passed away in 1991. If the population was 13,500 at the beginning of 2005, which expression gives its population at the end of 1998? 6 6 H 13,500 (1.008) F 13,500 (0.992) G

____

B

____

1 1 x 1 f 1 (x )   1 x f 1 (x ) 

f 1 (x )  log 3

x 1 2

J

13,500 (1.008)

C

f 1 (x )  1 

D

f 1 (x )  1 

H

f 1 (x ) 

6

1 ? x1

ˆ Ê 4. Which is the inverse of f (x )  2 ÁÁ 3 x  1 ˜˜ ? ¯ Ë x log 3 1 F f 1 (x )  2 G

____

6

3. Which is the inverse of f (x )  A

____

13,500 (0.992)

J

1 x 1 x

log 3 x  1 2 log 3 (x  1 ) f 1 (x )  2

5. If a m  b n , which of the following is NOT true? A

log a b n  m

C

B

log b a m  n

D

6. Evaluate log 0.125 4 F  3 2 G  3

3

m n m  log a b n / 2

log a b 

4. H J

1

4 9 2  9 

Name: ________________________

____

____

____

ÁÊ 1 7. Express log 4 18  ÁÁÁÁ log 4 36  2log 4 Ë2 1 A log 4 3 1 B log 4 2

ID: A

˜ˆ 3 ˜˜˜˜ as a single logarithm. ¯ C

log 4 6

D

log 4 27

8. Which is greatest? 200

F

log

2

4 20

H

log 25

G

log

3

81 8

J

log 0.5 16 50

C D

1.5 2

5

Ê log 8 ˆ˜ ˜˜ log 10 32  2 ÁÁÁ 10 ¯ Ë 9. Simplify . 16 log 2 2 A B

0.5 1

____ 10. Which of the following is equal to ÊÁË log 3 25 ˆ˜¯ ÊÁË log 4 log 75 F H log 12 G log 12 75 J ____ 11. Solve 4 2x  5  0.5 2  2x . 1 A x 2 7 B x 6 x ÁÊ 3 ˜ˆ ____ 12. Solve ÁÁÁÁ ˜˜˜˜  3. Ë2¯ ln 3 F ln 3  ln 2 ln 3 G ln 3  ln 2

3 ˆ˜¯ ?

log 5 log 2 log 2 5

C

x4

D

There is no solution.

H J

ln 3 1 ln 2 ln 3 1 ln 2

____ 13. What is the sum of the solutions of the equation log 2 (2  3x)  log 2 (4x  6)  2? 1 1 A  C 4 2 1 5 B D 4 4

2

Name: ________________________

ID: A

____ 14. Which is equal to 0.5e 2 ln x  2ln e x ? F

3x

H

x2  2x 2

G

x2 2

J

x2  x

____ 15. The graph shows a transformation of the graph of f(x)  2 x . What is the function represented by the graph?

A

f (x )  log 2 (x  1 )  1

C

h (x )  2 x  3  1

B

g (x )  2 3  x  1

D

h (x )  2 x  3  1

____ 16. The graph shows a transformation of the graph of f (x)  log 2 x . What is the function represented by the graph?

F G

a (x )  2 x  2  1 b (x )  log 2 (2  x)  2

H J

3

c (x )  log 2 (2  x)  2 d (x )  log 2 (x  3 )  1

Name: ________________________

ID: A

____ 17. If the data below is from an exponential function, what is the value of a?

A B

83 3 12

C D

8 3 16

____ 18. Which function is an example of exponential growth? x x G b (x )  2.4 (0.86) F a (x )  0.5 (1.2) ____ 19. Ted’s comic book collection, which was worth $1300 five years ago, has been increasing in value by 12% per year since then. Which expression gives the current value of the collection? 5 C 1300 (1.12) (5) A 1300 (1.12) È ˘ 5 B 1300 (.12) D 1300 ÍÍÍÎ 1  (.12) (5) ˙˙˙˚ ____ 20. The student population of Gloomy Valley High School has been steadily decreasing by 2% per year. If its population 8 years ago was 1200, which is the best expression for its population now? 8 8 G 1200 (.98) F 1200  1200 (.02) ____ 21. If g(x) is the inverse of f (x )  A (2, 3)

x 3  1 , which of the following is on g(x)? B (3, 2)

____ 22. Which is the inverse of f (x ) 

2x  5 ?

F

a (x )  x 2 

G

b (x ) 

5 2

(x  5 ) 2

H

c (x ) 

x2 5 2

J

d (x ) 

x2  5 2

f 1 (x ) 

2

____ 23. Which is the inverse of f (x )  6 x ? A

f 1 (x )  log x 6

C

B

f 1 (x )  log 6 x

D

log x 6 1 f (x )  6 log x

G

log 2 1024  10

B

5 3

H J

5log 6 log 128

____ 24. Which is the logarithmic form of 2 10  1024? F log 2 10  1024 ____ 25. Evaluate log 8 32 . 3 A 5 ____ 26. Express 2 log 4  3log 2 as a single logarithm. F 6log 8 G log 48

4

Name: ________________________

ID: A

____ 27. Which is the greatest? A log 2 32 8 B

log 3 27 13

____ 28. Simplify log 10 9  10 F 18

log 9

C

log 4 2 50

D

log 5 25 19

G

81

B

100 log 5

G

x2

C

x  2 log 3 30

D

x  log 3 60

.

____ 29. Which is equal to log 5 100? 2 A log 5 ____ 30. Solve 4 4x  5  8 3x  4 . 3 F x 2 ____ 31. Solve 3 2x  30. log 3 30 A x 2 B x  log 3 15

____ 32. Solve the equation log 2 (3x  1)  log 2 (x  7 )  5. F

x=1

____ 33. Which is equal to e ln 3  ln e 4 ? A 7

G

x=

B

12

25 or x = 1 3

____ 34. The graph of f (x)  2 x is transformed in the graph below. What functinon is represented by the graph?

F G

f (x )  2 x  3  1 g (x )  2 x  3  1

H J

5

h (x )  2 3  x  1 h (x )  2 3  x  1

Name: ________________________

ID: A

____ 35. The graph of f (x)  log 2 x is transformed in the graph below. What functinon is represented by the graph?

A B

a (x )  log 2 (x  3 )  2 a (x )  log 2 (x  3 )  2

C D

c (x )  log 2 (x  2 )  3 d (x )  log 2 (x  2 )  3

____ 36. If the data below is from an exponential function, what is the value of a?

F G

12 12.5

____ 37. Evaluate f (1) for f (x )  ln x . A 0

H J

13 13.5

B

1

____ 38. The data below is from an exponential function. What is the value of the constant ratio?

F G

1 1

H J

6

2 4

ID: A

Exponentials and Logarithms Multiple Choice Test Review 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. 33. 34. 35. 36. 37. 38.

B F B G D J A F B H C F A H B H A F A G B J B G B J A F A G A G A G B F A H

1