Kuta Software - Infinite Algebra 2
Name___________________________________
The Meaning Of Logarithms
Date________________ Period____
Rewrite each equation in exponential form.
1) log 6 36 = 2
1
= −2
196
3) log 14
2) log 289 17 =
1
2
4) log 3 81 = 4
Rewrite each equation in logarithmic form.
6) 12 2 = 144
1
2
5) 64 = 8
1
81
7) 9 −2 =
8)
( )
1
12
2
=
1
144
Rewrite each equation in exponential form.
15
=v
16
10) log v u = 4
11) log 7 x = y
12) log 2 v = u
9) log u
4
13) log u v = −16
14) log y x = −8
Rewrite each equation in logarithmic form.
15) u −14 = v
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16) 8 b = a
-1-
Worksheet by Kuta Software LLC
17)
()
1
5
x
y
=y
y
19) 9 = x
18) 6 = x
a
20) b = 123
Evaluate each expression.
21) log 4 64
23) log 4 16
22) log 6 216
24) log 3
1
243
25) log 5 125
26) log 2 4
27) log 343 7
28) log 2 16
29) log 3 27
30) log 5 25
31) log 64 4
32) log 6
1
216
Simplify each expression.
33) 12
35) x
log 12 144
log x 72
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34) 5
36) 9
-2-
log 5 17
log 3 20
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
The Meaning Of Logarithms
Date________________ Period____
Rewrite each equation in exponential form.
1) log 6 36 = 2
2) log 289 17 =
2
1
2
6 = 36
1
2
289 = 17
1
= −2
196
3) log 14
4) log 3 81 = 4
4
3 = 81
1
−2
14 =
196
Rewrite each equation in logarithmic form.
6) 12 2 = 144
1
2
5) 64 = 8
log 64
1
81
7) 9 −2 =
log 9
log 12 144 = 2
1
8=
2
8)
1
= −2
81
( )
1
12
2
log
=
1
12
1
144
1
=2
144
Rewrite each equation in exponential form.
15
=v
16
9) log u
10) log v u = 4
4
v =u
15
v
u =
16
11) log 7 x = y
4
y
()
7
4
u
2 =v
=x
13) log u v = −16
u
12) log 2 v = u
−16
14) log y x = −8
=v
y
−8
=x
Rewrite each equation in logarithmic form.
15) u −14 = v
16) 8 b = a
log u v = −14
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log 8 a = b
-1-
Worksheet by Kuta Software LLC
17)
()
1
5
x
y
=y
18) 6 = x
log 6 x = y
log 1 y = x
5
y
19) 9 = x
a
20) b = 123
log 9 x = y
log b 123 = a
Evaluate each expression.
21) log 4 64
22) log 6 216
3
3
23) log 4 16
2
24) log 3
1
243
−5
25) log 5 125
26) log 2 4
3
2
27) log 343 7
28) log 2 16
1
3
4
29) log 3 27
30) log 5 25
3
2
31) log 64 4
1
3
32) log 6
1
216
−3
Simplify each expression.
33) 12
log 12 144
34) 5
144
35) x
log x 72
log 5 17
17
36) 9
72
log 3 20
400
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-2-
Worksheet by Kuta Software LLC