Download M-370 5-3 HW Log Function.cwk (WP)

Section 5 – 3: The Logarithmic Function
log
x=a
b
Name ________________
a
is equivalent to x = b
Write in exponential form.
1.
log 4 (x) = y
2.
x = log(3)
4.
x = log 1 2 (y)
5. ln 6 = x
7.
5 = log x (y + 2)
8.
1
= log x (y)
2
3.
x = log 5 (y)
6.
log(y) = x
9.
1
= log y (x)
3
Convert each logarithmic equation to an exponential equation and solve for x.
10. log 2 (x) = 3
11. 3 2 = log 9 (x)
12. log 3 x = −2
13. log 3 (x) = 0
14. log(x) = −1
15. log x = −2
Math 370 Section 5 - 3
Page 1
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16. 2 3 = log 8 x
17. 3 2 = log16 x
18.
19. −3 2 = log 9 x
20. x = log3 27
21. x = log9 27
22. x = log4 32
23. x = log64 16
24. x = log7 7
26. log 3 (1 81) = x
27. log 2 (1 32) = x
29. log 3 1 = x
30. log x 81= 4
25.
x = log81 27
28. log 5 (1 5) = x
Math 370 Section 5 - 3
Page 2
−5 2 = log 4 x
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31. log x 64 = 3
32. log x 1= 6
34. log x 4 = 2 3
35
log x 5 = 1 3
36. log x (4 3) = −1 2
37. log x 25 = 2 3
38.
log 9 3 9 = x
39. log x 2 = 1 3
40. log x 16 = 4 3
41.
log 3
Math 370 Section 5 - 3
⎛ 1⎞
=x
⎝ 9⎠
Page 3
33. log x 7 = 1 2
⎛ 2⎞
42. log x
= −1 3
⎝ 3⎠
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Evaluate.
43. log 4 4
44.
log 5 25
46. log 2 1
47.
log 7
⎛ 1⎞
49. log 2 ⎜ ⎟
⎝ 8⎠
50. log 4
52.
53. ln e 3
ln e
Math 370 Section 5 - 3
45. log 3 81
⎛ 1⎞
⎝ 7⎠
48. log .01
⎛ 1⎞
⎝ 16⎠
51. log 5 5
Page 4
54.
ln (ln e)
© 2012 Eitel