Algebra 2
Evaluating Logarithms
Name: _____________________________
Period: _____
Use the definition of a logarithm to complete the table.
Exponential Form
Logarithmic Form
2.40  1
41.5  8
105  0.00001
log 4 0.0625  2
log x 8  3
52 
1
25
log   1
log100  2
Evaluate each expression.
1. log1000
2. log104
3. log1
4. log
1
10, 000
5. log103
6. log10
7. log 0.01
8. log
1
1000
When lumberjacks play music, why do they use a large
soup can instead of a bass drum?
Match each logarithmic expression with the value of x .
1. log 2 4  x
2. log 2 x  3
3. log 4 64  x
4. log 2 64  x
5. log x 81  2
6. log5 x  2
7. log x 7  1
8. log 4 x  
10. log7 x  1
11. log 64 x 
14. log x 1000  3
15. log 5
9. log8 x 
13. log 3
1
3
1
x
3
17. log x 4 
2
25. log13 169  x
3
33. log x
12. log5 x  4
2
x
5
16. log5 1  x
1
x
4
19. log 2 x  0
20. log8 x  
22. log108  x
23. log 4 x  1
24. log16 x 
18. log 2
21. log 1 x  1
29. log 2
1
2
2
2
3
1
2
26. log x 125 
3
4
27. log
3
2
3
1
2
28. log 1 x  2
x2
3
9
x
4
30. log x 0.1  1
31. log81 x 
1
 1
4
34. log a 1  x
35. log a a  x
1
4
32. log x 5 
1
2
36. log x 0.001  3
Answers
1
7
A. 2
B. 6
C.
L. 1
M. 3
N. 25
10.
36.
3.
15.
16.
5.
7.
11.
23.
D. 11
E. 4
F. 4
G. 625
H. 0
I.
O. 10
R. 1
S. 8
T. 2
U. 7
W.
27.
18.
14.
34.
1.
6.
31.
19.
2.
4.
25.
30.
12.
9.
35.
22.
24.
26.
20.
1
2
J. 5
1
4
Y. 9
33.
13.
21.
28.
17.
29.
8.
32.