Properties of Logarithms - Kuta Software
Kuta Software - Infinite Algebra 2
Properties of Logarithms
Expand each logarithm.
1) log (6 11)
( )6 5
3) log 11
24 5) log
5
x 7) log
y 6
u 4 9) log
v
3
11) log x y z
Name___________________________________ Date________________ Period____
2) log (5 3)
4) log (3 23)
( )6 6
6) log 5
8) log (a b)2
x 10) log
y 5
12) log (x y z2)
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Worksheet by Kuta Software LLC
Condense each expression to a single logarithm. 13) log 3 - log 8
log 6 14)
3
15) 4 log 3 - 4 log 8
16) log 2 + log 11 + log 7
17) log 7 - 2 log 12
2 log 7 18)
3
19) 6 log 3 u + 6 log 3 v
21) log 4 u - 6 log 4 v
23) 20 log 6 u + 5 log 6 v Critical thinking questions:
25) 2(log 2x - log y) - (log 3 + 2 log 5)
20) ln x - 4 ln y 22) log 3 u - 5 log 3 v 24) 4 log 3 u - 20 log 3 v 26) log x log 2
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Properties of Logarithms
Expand each logarithm.
1) log (6 11)
log 6 + log 11
( )6 5
3) log 11
5 log 6 - 5 log 11
24 5) log
5 4 log 2 - log 5
x 7) log
y 6 log x - 6 log y
u 4 9) log
v 4 log u - log v
3
11) log x y z
log x + log y + log z
3
3
3
Name___________________________________ Date________________ Period____
2) log (5 3)
log 5 + log 3
4) log (3 23)
log 3 + 3 log 2
( )6 6
6) log 5
6 log 6 - 6 log 5
8) log (a b)2
2 log a + 2 log b
x 10) log
y 5 log x - 5 log y
12) log (x y z2)
log x + log y + 2 log z
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Worksheet by Kuta Software LLC
Condense each expression to a single logarithm. 13) log 3 - log 8
3 log
8
log 6 14)
3
3
log 6
15) 4 log 3 - 4 log 8 34
log 84
17) log 7 - 2 log 12 7
log 122
19) 6 log 3 u + 6 log 3 v
log 3 (v6u6)
21) log 4 u - 6 log 4 v u
log 4 v6 23) 20 log 6 u + 5 log 6 v
( ) log 6 v5u20
Critical thinking questions:
25) 2(log 2x - log y) - (log 3 + 2 log 5)
4 x 2 log 75 y2
16) log 2 + log 11 + log 7 log 154
2 log 7 18)
3 log 3 72
20) ln x - 4 ln y x
ln y 4
22) log 3 u - 5 log 3 v u
log 3 v5 24) 4 log 3 u - 20 log 3 v
u 4 log 3 v20
26) log x log 2 Can't be simplified.
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at
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Worksheet by Kuta Software LLC
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