Accelerated Analysis
Name: _________________________________
Ch 11 Review
Date: ___________ Period: ________________
Chapter 11 Review
I. Simplify.
1. 4
2
2. 8
1
 1

4.  27 3  64 3 


2
4
3
9
5.  
 16 
3. 1000
 
1 .5
6. 27 5
II. Solve each equation by hand.
7. 3 y 

1
2
9. 3x  1
2
6

2
3

8. 9t 3  1  5
1
4

10.
5
x3  8

2
3
2
15
11. 91 x  27
12. 7 2 x 1  49 x 3
13. 8  16 2
14. 25
x
III. Rewrite
Rewrite as a logarithm.
15. 35 = 125
7
16. 2 = 128
x2
1
 
5
3 x 3
Rewrite as an exponential Equation
1
3
17. log5 25 = –2
18. log9 27 = 2
IV. Evaluate without a calculator.
1
16
19. log464
20. log164
21. log2
22. log99
23. log 2 8
24. log71
V. Expand each logarithm.
3
25. log10 a
34
b
26. log10
a2
b4
VI. Express as a logarithm of a single number or expression.
2
1
28. 5 log 4 x  log 4 y  log 4 3
28. log 6 m  log 6 n
2
3
VII. Given that log32 = 0.63 and log35 = 1.46, find the following:
15
31. log 3 20
32. log 3
33. log 3 100
2
27. log3 9ab3
30. 2 log 3 x  1
34. log 3 10
VIII. Simplify
log 3
35. 6 6
36. log 7 5  log 7 4  3 log 7 2
37. 3 log 2 4  1
38. log 100
39. log 18 1  log 7 7
40. ln 3 e
41. log 3 0
42. lne5
43. eln2
IX. Solve each equation by hand.
44. How do you solve an equation where the variable is raised to a fractional exponent?
45. How do you solve an equation where the variable is in the exponent?
X. Solve for x. Give your answer in calculator-ready form AND rounded to three significant figures.
1
46. 5 t  1  3
47. 4  5 x 
3
48. 63x = 42
49. 12 1 – x = 27
XI. Solve for x. Leave your answer in terms of e or natural logarithms.
50. ln e 5  x
51. ln( x  4)  1
52. e 3 x  27
53. 2ex – 2 =30
XII. Solve for x.
54. log x 4  
1
2
56. 2 log 5 x  log 5 4  log 5 16
58. log 10 a  log 10 a  21  2
55. log 4 x  log 4 ( x  6)  log 4 5
57. log 10 y 
59. log 5 x  4  0
1
1
log 10 16  log 10 49
4
2
60. log 3 27  x
XIII. Use a calculator to find each value of x. Give answers to three significant digits
61. log x  3.62
62. log x  0.00745
XIV. Find to three significant digits. (Use your calculator)
64. log 5 7
65. log 2 8
63. log x  2