Math 623
Name_________________________
Logarithm Worksheet I
For the problems below:
i.
ii.
Fill in the blanks with the appropriate number
Rewrite in either exponential or logarithmic form as necessary
EXPONENTIAL FORM
1.
43 = _______
2.
4-3 = ________
3.
4 2 = ________
4.
4
5.
4 2 = ________
6.
4
7.
80 = ________
8.
8
LOGARITHMIC FORM
1
− 12
= ________
3
− 32
− 13
= ________
= ________
9.
log864 = ________
10.
log2________ = -3
11.
log8________ =
12.
log_______64 = 3 (find the base)
2
3
How would you read the statements below? Are the statements true? Why?
Example:
log2.25 = -2
13.
log10100 = 2
14.
log5125 = 3
“Log base 2 of .25 is –2”
Yes this is true since, 2− 2 =
1 1
= = .25
22 4
Evaluate each function below. (Note: the best way to do this is to rewrite the expression in exponential
form.) If no base is specified, then assume it is “base 10.”
15. log24 =
16.
log28 =
17.
log42 =
18.
log1010 =
19.
log(.1) =
20.
log327 =
21.
log3 ⎛⎜ 1 ⎞⎟ =
⎝ 27 ⎠
22.
log21 =
23.
log8 ⎛⎜ 1 ⎞⎟ =
⎝2⎠
24.
log164 =
25.
log2128 =
26.
log2 ⎛⎜ 1 ⎞⎟ =
⎝8⎠
Solve each equation for the variable. (Again, you will first want to rewrite the expression in
exponential form.)
27.
log3n = 6
28.
log10n = -4
29.
log648 = x
30.
log864 = x
31.
logy ⎛⎜ 1 ⎞⎟ = −1
⎝ 3⎠
32.
logt64 = 3
33.
log4x = 3
34.
logx81 = 4
35.
log81 = y
36.
log108 = -2
37.
logm2 =
38.
log232 = x
39.
log3x = 3
40.
logx27 =
1
3
3
2