Kuta Software - Infinite Algebra 2
Name___________________________________
Properties of Logarithms
Date________________ Period____
Expand each logarithm.
1) log (6 ⋅ 11)
5
2) log (5 ⋅ 3)
4) log (3 ⋅ 2 3 )
3) log
( )
5) log
2
5
6) log
x
8) log (a ⋅ b) 2
6
11
4
7) log
y
()
6
6
4
u
9) log
v
11) log
6
5
3
10) log
x⋅ y⋅z
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x
y5
12) log ( x ⋅ y ⋅ z 2 )
-1-
Worksheet by Kuta Software LLC
Condense each expression to a single logarithm.
13) log 3 − log 8
15) 4 log 3 − 4 log 8
17) log 7 − 2 log 12
14)
log 6
3
16) log 2 + log 11 + log 7
18)
2 log 7
3
19) 6 log 3 u + 6 log 3 v
20) ln x − 4 ln y
21) log 4 u − 6 log 4 v
22) log 3 u − 5 log 3 v
23) 20 log 6 u + 5 log 6 v
24) 4 log 3 u − 20 log 3 v
Critical thinking questions:
25) 2(log 2 x − log y) − (log 3 + 2 log 5)
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26) log x ⋅ log 2
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Properties of Logarithms
Date________________ Period____
Expand each logarithm.
1) log (6 ⋅ 11)
2) log (5 ⋅ 3)
log 6 + log 11
3) log
( )
6
11
5
log 5 + log 3
4) log (3 ⋅ 2 3 )
log 3 + 3 log 2
5 log 6 − 5 log 11
4
5) log
2
5
6) log
4 log 2 − log 5
7) log
6
6 log 6 − 6 log 5
8) log (a ⋅ b) 2
x
y
()
6
5
6
2 log a + 2 log b
log x − 6 log y
4
u
9) log
v
10) log
4 log u − log v
11) log
3
x⋅ y⋅z
y5
log x − 5 log y
12) log ( x ⋅ y ⋅ z 2 )
log x log y log z
+
+
3
3
3
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x
log x + log y + 2 log z
-1-
Worksheet by Kuta Software LLC
Condense each expression to a single logarithm.
13) log 3 − log 8
log
3
8
3
log 6
3
log
15) 4 log 3 − 4 log 8
log
14)
3
6
16) log 2 + log 11 + log 7
4
log 154
84
17) log 7 − 2 log 12
18)
7
log
12
3
2
19) 6 log 3 u + 6 log 3 v
log 4
7
log
2
20) ln x − 4 ln y
log 3 (v 6 u 6 )
21) log 4 u − 6 log 4 v
2 log 7
3
ln
x
y4
22) log 3 u − 5 log 3 v
u
log 3
v6
u
v5
23) 20 log 6 u + 5 log 6 v
24) 4 log 3 u − 20 log 3 v
log 6 (v 5 u 20 )
u4
log 3
v
20
Critical thinking questions:
25) 2(log 2 x − log y) − (log 3 + 2 log 5)
log
26) log x ⋅ log 2
4x2
75 y 2
Can't be simplified.
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-2-
Worksheet by Kuta Software LLC