ExamView - Chapter 3 semester exam review.tst

Name: ________________________ Class: ___________________ Date: __________

ID: A

Chapter 3 Review for semester exam Short Answer 1. Solve for x .

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

equation for x . ÊÁ 1 ˆ˜ ÁÁÁ ˜˜˜ ÁÁÁ 4 ˜˜˜  1, 024 Ë ¯ x

3 x  1  243

7. Write the logarithmic equation in exponential

2. Solve for x . Approximate the result to three

form.

decimal places. log4 x 

log6 216  3

1 2

8. Evaluate the function f(x)  1.1 at x  3.6 . x

Round to 3 decimal places.

3. Solve the logarithmic equation algebraically.

Approximate the result to three decimal places. 4 log2 (0.5x )  13

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

following equation for x. 2 5x  128 4. Use the graph of f to determine the

transformation that yields the graph of g . 10. Write the exponential equation in logarithmic

f (x )  2 x , g (x )  2 x  7

form. 8 2 

5. Condense the expression log5 x  log5 7 to the

logarithm of a single term.

1

1 64

Name: ________________________

ID: A

11. Evaluate the function at the indicated value of

17. Find the exact value of the logarithmic

xb .

expression without using a calculator.

g (x )  logb x

log5 125

6

18. Use the properties of logarithms to expand the

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

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

equation for x. log5 (7x  4)  log5 10

log5

x

2

2 3

y z

13. Use the properties of logarithms to simplify the

expression. 2

log 2 14

19. Evaluate the function at the indicated value of

x  1.

f (x )  log9 x 14. Use the properties of logarithms to rewrite and

simplify the logarithmic expression. Ê 4 8ˆ log2 ÁÁÁ 4  5 ˜˜˜ Ë ¯

20. Condense the expression to the logarithm of a

single quantity. 1È ÍÍ log (x  2 )  2 log (x  2 ) ˘˙˙  4 log x ˙˚ ÍÎ 3 3 3 2

ÊÁ 1 ˆ˜ 3 ˜˜˜ . 15. Simplify the expression log3 ÁÁÁÁ ˜ 27 Ë ¯

21. Find the exact value of log8

3

64 without using

a calculator.

16. Rewrite the logarithm as a ratio of common

logarithms. log5 18

22. Find the exact value of log4 44  log4 11 without

using a calculator.

2

ID: A

Chapter 3 Review for semester exam Answer Section SHORT ANSWER 1. ANS:

5

PTS: 1 2. ANS:

REF: 3.4.16

4 2 PTS: 1 3. ANS:

Ê 13 2 ÁÁÁÁ 2 Ë

4

REF: 3.4.24

˜ˆ˜˜  19.027 ˜¯

PTS: 1 4. ANS:

REF: 3.4.97

Shift the graph of f seven units upward. PTS: 1 5. ANS:

REF: 3.1.23

PTS: 1 6. ANS:

REF: 3.3.71

PTS: 1 7. ANS:

REF: 3.1.51

log5 7x

OBJ: Condense logarithmic function using the properties of logs

x4

6 3  216 PTS: 1 8. ANS:

REF: 3.2.8

1.409 PTS: 1 9. ANS:

REF: 3.1.7

OBJ: Raise number to a non-integer power

REF: 3.1.52

OBJ: Solve exponential equations using one-on-one property

7 5 PTS: 1

1

ID: A 10. ANS:

log8

1

64

 2

PTS: 1 11. ANS:

REF: 3.2.19

PTS: 1 12. ANS:

REF: 3.2.28

6

6 7 PTS: 1 13. ANS:

REF: 3.2.88

14 PTS: 1 14. ANS:

REF: 3.2.36

PTS: 1 15. ANS:

REF: 3.3.24

8  8 log2 5

–9 PTS: 1 16. ANS:

REF: 3.3.26

OBJ: Simplify logarithmic functions

log18 log5 PTS: 1 17. ANS:

REF: 3.3.7a

PTS: 1 18. ANS:

REF: 3.3.29

PTS: 1 19. ANS:

REF: 3.3.63

3

2 log5 x  2 log5 y  3 log5 z

0 PTS: 1

REF: 3.2.25

2

ID: A 20. ANS:

log3

(x  2 ) x  2 x

4

PTS: 1 21. ANS:

REF: 3.3.84

PTS: 1 22. ANS:

REF: 3.3.32

OBJ: Evaluate logarithmic function using properties of logarithms

REF: 3.3.43

OBJ: Evaluate logarithmic function using properties of logarithms

2 3

1 PTS: 1

3