Condense the expression. 1. 5 log332â 2log3x +. 1. 2 log3y. 21. Condense: 4 log x â 6 log (x + 2). 22. Use the properties of logarithms to evaluat...

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Pre-Calculus: Chapter 3 Review 3. y = log 2 (x + 1 )

Graph the function. State the domain and range. 1. f (x ) = 4 x

.

.

4. y = log 2 x − 3

2. y = log 3 x

Write the equation in logarithmic form. 5. 6 4 = 1, 296

4

6. 125 3 = 625

1

A

A

7. Write the equation log 32 8 =

16. Expand: log 3 11p 3

3 in exponential form. 5

8. Write the equation log 243 729=

6 in exponential 5

17. Expand: log b

57 74

18. Expand: log 7

9a 5b

form.

9. Evaluate without using a calculator. log 2 16

10. Evaluate without using a calculator. log 7

1 49

19. Condense the expression.

1 log 16 − 3log 5 x + 4log5 y 2 5

20. Condense the expression. 1 1 log 32 − 2log 3 x + log 3 y 5 3 2

11. Evaluate the expression. log 1/5 125

12. Evaluate ln e −4 . 21. Condense: 4 log x − 6 log (x + 2)

13. Evaluate ln

3

e −5 . 22. Use the properties of logarithms to evaluate log 3 9 + log 3 36 − log 3 4 .

14. Evaluate: log 0.01 23. Condense: 3 ln 3 + 3 lnc 15. Expand the expression. ln

2x y4 24. Condense: 3 ln a −

2

1 (ln b + ln c 2 ) 2

A 25. Solve: log 4 (x + 3 ) = −2

35. Solve ln x − ln 6 = 0 .

26. Solve: log 4 (x + 6 ) + log 4 x = 2

36. Solve: 6e 4x − 2 = 3

27. Solve: 7log 5 (x ) − 3 = 15

37. Solve: e x =

28. Solve:

1 = 644x − 3 . 16

29. Solve:

1 = 9 8x − 9 27

3 4

38. Solve: 6 4x = 63

30. Solve: log(4x + 10) = 3 .

31. Solve: 3 log 2x = 4.

32. Solve: log(x + 9) − log x = 3 .

33. Solve: ln(2x − 1) = 8.

34. Solve ln 2 + ln x = 5.

3

ID: A

Pre-Calculus: Chapter 3 Review Answer Section

1. 2.

3. Domain: x > −1; Range: all real numbers

1

ID: A 4.

5. log 6 1, 296 = 4 6. log 125 625 =

4 3

3

7. 32 5 = 8 8. 9. 10. 11. 12. 13. 14. 15. 16.

243 6/5 = 729 4 –2 −3 -4 −5 3 –2 ln2 + lnx − 4lny log 3 11 + 3 log 3 p

1 1 log b 57 − log b 74 2 2 1 1 1 1 18. log 7 9 + log 7 a − log 7 5 − log 7 b or 2 2 2 2 1 1 1 log 7 3 + log 7 a − log 7 5 − log 7 b 2 2 2 17.

19. log 5 20. log 3

4y 4 x3 2

y

x2 21. none of these 22. 4 23. ln 27c 3

2

ID: A

24. ln 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.

a3

c b 47 − 16 2 62.712 7 12 15 16 495 2 10.7722 0.0090 1,490.979 74.2 6 –0.046 –0.288 0.58

3