Write Each Expression As a Single Logarithm

Name Class Date

Practice Form

Properties of Logarithms 7-4 G

Write each expression as a single logarithm. log 4+ log 3 log 25- log 5 log 4+ log 2 - log 8 1. 5 5 2. 6 6 3. 2 2 2

5logx= 2log x log 60- log 4 + log x 4. 7 7 5. 4 4 4 6. log 7 − log 3 + log 6

1 1 1 7. 2 log x − 3 log y 8. logr+ log s - log t 9. log3 4x + 2 log3 5y 2 3 4

1 2 log 3x+ log 3 x 10. 5 log 2 − 2 log 2 11. 3 3 12. 2 log 4 + log 2 + log 2

log 3- log 6 13. (log 3 − log 4) − log 2 14. 5 log x + 3 log x2 15. 6 6

1 log 2x- 5log y (logx- log y ) 16. log 2 + log 4 − log 7 17. 3 3 18. 3 2 2

1 1 19. logx+ log y - 2log z 20. 3(4 log t2) 21. logy- 4(log r + 2log t ) 2 3 5 5 5

Expand each logarithm. Simplify if possible.

x 3 22. log xyz 23. log2 24. log 6x y yz

2rst 5x 25. log 7(3x − 2)2 26. log 27. log 5w 4y

2x2 y 28. log 5x-5 29. log 30. log (3xyz )2 5 3k 3 4 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?

Practice (continued) Form

Properties of Logarithms 7-4 G

Determine if each statement is true or false. Justify your answer. 3 log3 40. log 12 = log 4 + log 3 41. log = 5 log5

1 42. log 12+ log 3 = 2 43. log 4x= log 2 x 6 6 2 4 4

Use the properties of logarithms to evaluate each expression.

44. log2 8+ log 2 4 45. log2 160- log 2 5 46. log6 27+ log 6 8

1 4 log7 14- log 7 2 log4 64+ 2log 4 2 log3 162- log 3 2 47. 48. 49. 4

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

1 2 20 53. logx= log 3 x 54. log7= log3 49 55. log 20- 3logx = log 3 2 2 3 4 4 4 x3 I The formula for loudness in decibels (dB) is L = 10 log , where I is the intensity of a I0 2 − 12 2 sound in watts per square meter (W/m ) and I0 is 10 W/m , 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 − 12 2 decibels? Use I0 = 10 W/m .

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