Name
7-4
Class
Date
Practice
Form G
Properties of Logarithms
Write each expression as a single logarithm.
1. log 5 4 + log 5 3
2. log 6 25 − log 6 5
3. log 2 4 + log 2 2 − log 2 8
4. 5log 7 x = 2 log 7 x
5. log 4 60 − log 4 4 + log 4 x
6. log 7 − log 3 + log 6
7. 2 log x − 3 log y
8.
10. 5 log 2 − 2 log 2
11.
13. (log 3 − log 4) − log 2
14. 5 log x + 3 log x2
15. log 6 3 − log 6 6
16. log 2 + log 4 − log 7
17. log 3 2 x − 5log 3 y
18.
19.
1
1
log x + log y − 2 log z
2
3
1
1
1
log r + log s − log t
2
3
4
1
2
log 3x + log 3x
3
3
2
9. log3 4x + 2 log3 5y
12. 2 log 4 + log 2 + log 2
1
(log 2 x − log 2 y )
3
21. log5 y − 4(log5 r + 2 log5 t )
20. 3(4 log t )
Expand each logarithm. Simplify if possible.
23. log 2
22. log xyz
25. log 7(3x − 2)
2
26. log
28. log5 5x−5
29. log
x
yz
24. log 6x3 y
2rst
5w
27. log
2 x2 y
3k 3
5x
4y
30. log4 (3xyz)2
Use the Change of Base Formula to evaluate each expression. Round your answer to the
nearest thousandth.
31. log 4 32
32. log 3 5
33. log 2 15
34. log 6 17
35. log 6 10
36. log 5 6
37. log 8 1
38. log 9 11
39. The concentration of hydrogen ions in a batch of homemade ketchup is 10
−4
pH level of the ketchup?
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33
. What is the
Name
7-4
Class
Date
Practice (continued)
Form G
Properties of Logarithms
Determine if each statement is true or false. Justify your answer.
3 log 3
40. log 12 = log 4 + log 3
41. log =
5 log 5
42. log 6 12 + log 6 3 = 2
43.
1
log 4 4 x = log 4 2 x
2
Use the properties of logarithms to evaluate each expression.
44. log 2 8 + log 2 4
45. log 2 160 − log 2 5
46. log 6 27 + log 6 8
47. log 7 14 − log 7 2
48. log 4 64 + 2 log 4 2
49.
1
log 3 162 − log 3 4 2
4
State the property or properties used to rewrite each expression.
50. log 6 − log 3 = log 2
1
3
53. log 2 x = log 2
3
51. 6 log 2 = log 64
x
54.
2
log 7 = log 3 49
3
52. log 3x = log 3 + log x
55. log 4 20 − 3log 4 x = log 4
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.
The formula for loudness in decibels (dB) is L = 10 log
25
2
56. A sound has an intensity of 5.92 × 10 W/m . 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?
⎛ 9 ⎞
⎝ 4 ⎠
58. Writing Explain why ⎜ ⎟ ≠
log9
.
log 4
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34
20
x3