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Name ____________________________________________
Algebra II & Trigonometry
A2.A.28
Date ______________________________________
Logarithmic Form of an Equation
Solve a logarithmic equation by rewriting as an exponential equation
In 1 – 12, write each exponential equation in logarithmic form.
1. 24  16
2. 32  9
1
1
3. 10 2  0.01
4. 12 0  1
1
6

1
2
1
3
5. 8 3  2
6. 5 2  5
7. 6 1 
9. 4a  b
10. x 3  y
11. 5c  d
12. b a  8
14. log7 49  2
15. log10 1000  3
16. log27 9 
18. log15 1  0
19. log 1 3  
8. 9

In 13 – 24, write each logarithmic equation in exponential form.
13. log2 64  6
17. log4 32 
5
2
21. log10 0.001  3
9
22. loga 3 a 
1
3
23. loga
In 25 – 33, solve each equation for x.
25. log2 x  4
26. log5 x  2
28. log7 x  0
29. log81 x 
31. log6 x  2
32. log10 x  7
1
2
1
2
20. log 1 2  
8
1
 1
a
24. logb c 
27. log3 x  2
30. log9 x  
33. log64 x 
2
3
1
2
2
3
1
5
1
3
In 34 – 42, evaluate each expression.
34. log3 27
37. log5
1
25
40. log36 216
35. log2 16
36. log10 10000
38. log8 32
39. log100 0.1
41. log49
1
7
42. log27
1
9
45. logb
1
 1
2
In 43 – 51, solve each equation for b.
43. logb 27  3
46. logb 125 
44. logb 49  2
3
2
49. logb 0.1  
1
2
47. logb 4 
1
2
50. logb 8  3
48. logb 6 
1
3
51. logb 5 
1
4