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Algebra 2/Trig
Unit 11: Exponential and Logarithmic Functions
Name: _______________________
Date: ___________
For problems # 1 – 8, state whether the function represents exponential growth or exponential decay.
1
1. f ( x)  4  
 3
5.
x
2.
4
f ( x)   
3 x
1
6. f ( x)  3  
5
f ( x)  4(2) x
f ( x)  4 x
3.
x
4.
7.
8.
Match the expression with the logarithm in the box that has the same value.
9. log 4 +log 3
10. log 3  log4
11. 3 log 4
______
______
13. log 2  log 8
14. log 4  log10
______
A. log
______
2
B. log 81
5
E. log 64
12. 4 log 3
______
______
15. 2log 4  log 2
16. 3log 1
______
______
C. log
F. log 27
f ( x)  2(0.15) x
3
D. log 8
4
G. log12
3
H. log 4
Write each equation in exponential form.
18. log 25 5 
17. log6 216  3
1
2
19. log 3
1
 4
81
20. log 32 8 
Write each equation in logarithmic form.
3
21. 5  125
22. 7  1
3
0
1
1
23.   
 4  64
Evaluate each expression.
25. log3 81  y
29. log8 4  y
26. log 2
1
y
16
30. log 6 64  y
27. log 1 27  y
3
31. log 3
1
3
28. log9 1  y
24. 34 
1
81
3
5
Solve each equation or inequality. Check for extraneous solutions.
32. log10 n  3
34. log 4 x 
33. log 4 x  3
3
2
35. log 1 x  3
5
1
 3
8
36. log 7 q  0
37. log6 (2 y  8)  2
38. log n
40. 36 n 5  94 n 3
41. 92 x 1  27 x  4
1
42. 23n1   
8
39. 7 6 x  7 2 x 20
n
43. log3 ( x 2  2)  log3 x
44. log 7 (8 x  20)  log 7 ( x  6)
Use the product, quotient, or power properties to find the approximate value of each expression.
log4 5 = 1.1610
log4 3 = 0.7925
45.
log4 15
46.
log4 53
47. log4
5
3
Use the properties of logarithms to solve each equation or inequality. Check for extraneous solutions.
2
48. log 7 n  log 7 8
49. log6 x  log6 9  log6 54
50. log9 (3u  14)  log9 5  log9 2u
3
51. log10 (3m  5)  log10 m  log10 2
52. log8 (t  10)  log 8 (t 1)  log 8 12
53. log10 (r  4)  log10 r  log10 (r  1)
54. log10 4  log10 w  2
Set up the change-of-base formula for each. (you do not need to evaluate)
55. log5 12
56. log8 32
57. log9 6