Download 5-5 HW Properties Of Logarithms

Section 5 – 5: Properties of Logarithms
Product Property
Name ______________________
Power Property
logb ( x ) a = a• logb (x)
logb (x • y) = logb (x) + logb (y)
Quotient Property
⎛ x⎞
logb ⎜ ⎟ = logb (x) − log b (y)
⎝ y⎠
Express as the sum, difference and/or product of logarithms.
1.
log 2 (5x )
( )
4. ln xy 3
7. log 4
(3 x )
⎛ x2 ⎞
10. log⎜ 3 ⎟
⎝y ⎠
Math 370 Section 5 - 5
2.
log 3 ( xy )
(
5. log x 2 y 3
3.
)
(
6. log 3 81xy 2
)
⎛ x4 ⎞
9. log 5 ⎜ 2 ⎟
⎝y ⎠
8. log (x y )
11.
log 2 (9xy)
⎛ ax 3 ⎞
log 2 ⎜ 4 ⎟
⎝y ⎠
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⎛ y⎞
12. log⎜ 3 ⎟
⎝ x⎠
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Properties of Logs
Product Property
Power Property
Quotient Property
⎛ x⎞
logb (x) − logb (y) = log b ⎜ ⎟
⎝ y⎠
a• logb (x) = logb ( x )a
logb (x) + logb (y) = logb (x • y)
Write as a single logarithm.
13. 4log 3 x + log 3 y
14. 3log 5 x + 2log 5 y
15. 3log2 + 5log y
16. 2log 4 5 + 3log 4 x
17. 2log 5 x + 3log 5 4
18. log 2 3 + log 2 (2x − 5)
19.
3log 5 2 + log 5 (3x + 4)
20.
log x + log( x − 3)
21. 2log 3 3 + log 3(2x − 3)
22.
log 3 x 2 + log 3 (x 2 + 4x)
23.
3log 4 x + log 4 (2x − 1)
24. log 4 3 + log 4 x + log4 (x − 2)
25. log(x + 1) + log(x − 3)
26. log 7 (x + 2) + log 7 (x − 2)
Math 370 Section 5 - 5
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27.
log 4 (x − 2) + log4 (x − 5)
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28. log(3x + 2) + log(x − 1)
29. log 4 (2x + 1) + log4 (3x + 2)
30.
31. 2log 4 − 2log x
32. 2log 5 x − 3log 5 y
33. 4log 5 x − log 5 (x − 3)
34. log 3(2x − 1) − 2log 3 x
35. 3log 2 (2) − log2(3x − 4)
36. log 4 (x − 3) − log 4 (x 2 − 9)
37.
1
log(x) − 3log 2
2
Math 370 Section 5 - 5
38.
1
log 3(x − 3) − log 3(x)
2
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39.
log 5(2x − 1) + log5 (4 x − 3)
1
log (x − 1) − 2log 3 3
3 3
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Find the domain of each function.
⎛2
⎞
x−7
⎝3
⎠
40. f (x) = log 3 (2x − 5)
41. h(x) = log 3(−7 x + 3)
42. m(x) = log 3
43. k(x) = ln x 3
44. h(x) = log 4 x 2
45. h(x) = 2log 4 x
46. f (x) = ln x
47. h(x) =
Math 370 Section 5 - 5
1
ln x
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48. k(x) = ln(ln x)
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49. m(x) = ln x
51. h(x) = log 2
53. f (x) = ln
⎛ 1 ⎞
⎝ x + 3⎠
50. m(x) = log 5
⎛ x + 4⎞
⎝ 5 ⎠
⎛ 1 ⎞
⎝ x − 3⎠
Math 370 Section 5 - 5
52. m(x) = ln
⎛ x − 2⎞
⎝ 3 ⎠
54. f (x) = log 2
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⎛ −2 ⎞
⎝ x + 4⎠
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Find the Inverse f −1 (x) for each function:
55. f (x) = log 3 ( x)
56. f (x) = log 6 ( x )
57. f (x) = log ( x)
58. f (x) = ln ( x)
59. f (x) = log 6 ( x + 1)
60. f (x) = log ( x) + 1
61. f (x) = 3x
62. f (x) = 5 x
63. f (x) = 10 x
64. f (x) = e x
65. f (x) = e x+1
66. f (x) = e x + 1
Math 370 Section 5 - 5
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© 2012 Eitel