Properties of Logarithms

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Class

7-4 Practice Properties of Logarithms

Write each expression as a single logarithm.

1. log5 4 log5 3

2. log6 25 log6 5

4. 5log7 x 2 log7 x 7. 2 log x - 3 log y 10. 5 log 2 - 2 log 2

5. log4 60 log4 4 log4 x

8. 1 log r 1 log s 1 log t

2

3

4

11. 1 log 3x 2 log 3x

3

3

Date

Form G

3. log2 4 log2 2 log2 8 6. log 7 - log 3 + log 6 9. log3 4x + 2 log3 5y 12. 2 log 4 + log 2 + log 2

13. (log 3 - log 4) - log 2

14. 5 log x + 3 log x2

15. log6 3 log6 6

16. log 2 + log 4 - log 7

17. log3 2x 5log3 y

19. 1 log x 1 log y 2 log z 20. 3(4 log t2)

2

3

18.

1 3

(log

2

x log2

y)

21. log5 y 4(log5 r 2 log5 t)

Expand each logarithm. Simplify if possible.

22. log xyz

23.

log2

x yz

24. log 6x3 y

25. log 7(3x - 2)2

2rst 26. log

5w

27. log 5x 4y

28. log5 5x5

2x2 y 29. log

3k 3

30. log4 (3xyz)2

Use the Change of Base Formula to evaluate each expression. Round your answer to the nearest thousandth.

31. log4 32

32. log3 5

33. log2 15

34. log6 17

35. log6 10

36. log5 6

37. log8 1

38. log9 11

39. The concentration of hydrogen ions in a batch of homemade ketchup is 10 - 4. What is the pH level of the ketchup?

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Name

Class

7-4 Practice (continued) Properties of Logarithms

Determine if each statement is true or false. Justify your answer.

40. log 12 = log 4 + log 3

41. log 3 log3 5 log5

Date

Form G

42. log6 12 log6 3 2

1 43. 2 log4 4x log4 2x

Use the properties of logarithms to evaluate each expression.

44. log2 8 log2 4

45. log2 160 log2 5

46. log6 27 log6 8

47. log7 14 log7 2

48. log4 64 2 log4 2

49.

1 4

log3

162

log3

4

2

State the property or properties used to rewrite each expression.

50. log 6 - log 3 = log 2

51. 6 log 2 = log 64

52. log 3x = log 3 + log x

53.

1 3 log2

x

log2

3

x

54. 2 log 7 log 3 49 3

20 55. log4 20 3log4 x log4 x3

The formula for loudness in decibels (dB) is L = 10 log I , where I is the intensity of a I0

sound in watts per square meter (W/m2) and I0 is 10 - 12 W/m2, the intensity of a barely audible sound.

56. A sound has an intensity of 5.92 1025 W/m2. What is the loudness of the sound in decibels? Use I0 = 10 - 12 W/m2.

57. Suppose you decrease the intensity of a sound by 45%. By how many decibels would the loudness be decreased?

58.

Writing

Explain

why

9 4

log 9 log 4

.

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