ID: 1
Algebra 2 - Task 7.2
Name___________________________________
Expanding and Condensing Logarithms
Date________________ Period____
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Expand each logarithm. Justify each step by stating logarithm property used.
Level 2:
1) log 6
u
v
3) log 7 5
3
2) log 5
4
4) log 4 u
5) log (a ⋅ b)
6) log 5
a
6
6
7
Level 3:
7) log 4
x
8) log 6 (3 ⋅ 11)
3
6
10) log 4 (a ⋅ b ⋅ c)
9) log 6 (ab 3 )
11) log 5 (10 ⋅ 11
3
)
12) log 7 ( x ⋅ y)
6
Level 4:
13) log 2 ( x ⋅ y)
3
15) log 9 (z
14) log 3 (z
3
x ⋅ y)
17) log 8 ( x ⋅ y)
3
16) log 8
2
18) log 2
4
()
()
a
x)
5
b4
a
2
b4
Condense each expression to a single logarithm. Justify each step by stating the logarithm property used.
Level 2:
19) 6 log 5 10
21) log 7 u − log 7 v
log x
3
22) log 6 x − log 6 y
23) log 4 2 + log 4 7
24) log 3 a + log 3 b
20)
Level 3:
25) 5 log 7 11 − log 7 8
26) log 3 x + 2 log 3 y
27) 2 log 8 x
28) 2 log 9 a
29) log u + log v + log w
30) log 2 12 + log 2 7 + log 2 5
Level 4:
31)
33)
log 5 x
+
2
log 7 x
log 5 y
+
2
+
log 7 y
log 5 z
32) 3 log 6 a − 6 log 6 b
2
+
log 7 z
3
3
3
35) 3 log 3 u + 15 log 3 v
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34) 3 log 4 a − 3 log 4 b
36) 3 log 5 u + 12 log 5 v
Worksheet by Kuta Software LLC
ID: 1
Algebra 2 - Task 7.2
Name___________________________________
Expanding and Condensing Logarithms
Date________________ Period____
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Expand each logarithm. Justify each step by stating logarithm property used.
Level 2:
log 5 a
3
u
2) log 5 a
1) log 6
log 6 u − log 6 v
3
v
3) log 7 5
4
4 log 7 5
4) log 4 u
5) log (a ⋅ b) log a + log b
6) log 5
6
6 log 4 u
6
log 5 6 − log 5 7
7
Level 3:
7) log 4
x
3
3 log 4 x
6
8) log 6 (3 ⋅ 11) 6 log 6 3 + 6 log 6 11
2
9) log 6 (ab 3 ) log 6 a + 3 log 6 b
3
11) log 5 (10 ⋅ 11 ) log 5 10 + 3 log 5 11
10) log 4 (a ⋅ b ⋅ c) log 4 a + log 4 b + log 4 c
12) log 7 ( x ⋅ y)
6
6 log 7 x + 6 log 7 y
Level 4:
13)
3
3
log 2 ( x ⋅ y)
9 log 2 x + 3 log 2 y
log 9 x log 9 y
x ⋅ y ) log 9 z +
+
2
2
15) log 9 (z
17) log 8 ( x ⋅ y)
3
14) log 3 (z
16) log 8
2
6 log 8 x + 2 log 8 y
18) log 2
4
()
()
a
x ) 4 log 3 z +
2
5
5 log 8 a − 20 log 8 b
b4
a
log 3 x
2
2 log 2 a − 8 log 2 b
b4
Condense each expression to a single logarithm. Justify each step by stating the logarithm property used.
Level 2:
19) 6 log 5 10 log 5 10 6
log x
3
log x
3
x
22) log 6 x − log 6 y log 6
y
24) log 3 a + log 3 b log 3 ba
20)
u
v
23) log 4 2 + log 4 7 log 4 14
21) log 7 u − log 7 v log 7
Level 3:
11 5
25) 5 log 7 11 − log 7 8 log 7
8
2
27) 2 log 8 x log 8 x
26) log 3 x + 2 log 3 y log 3 ( x y 2 )
28) 2 log 9 a log 9 a
29) log u + log v + log w log wvu
2
30) log 2 12 + log 2 7 + log 2 5 log 2 420
Level 4:
31)
33)
log 5 x
+
2
log 7 x
log 5 y
+
2
+
log 7 y
log 5 z
2
+
log 7 z
log 5
log 7
3
3
3
35) 3 log 3 u + 15 log 3 v log 3 (v 15 u 3 )
zyx
3
zyx
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32) 3 log 6 a − 6 log 6 b log 6
34) 3 log 4 a − 3 log 4 b log 4
a
3
b6
a
3
b3
36) 3 log 5 u + 12 log 5 v log 5 (v 12 u 3 )
Worksheet by Kuta Software LLC
ID: 2
Algebra 2 - Task 7.2
Name___________________________________
Expanding and Condensing Logarithms
Date________________ Period____
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Expand each logarithm. Justify each step by stating logarithm property used.
Level 2:
3
1) log 7
10
2) log 9 11
u
3) log 8
v
4) log 3
9) log 4
x
6) log 8 ( x ⋅ y)
3
5) ln x
Level 3:
7) log 3
3
5
4
()
( )
x
y
7
12
4
8
8) log 4
7
10) log 6 (a ⋅ b ⋅ c)
5
3
x5
11) log 5
y
Level 4:
12) log 6
2
14) log 8 ( x ⋅ y ⋅ z
5 6
13) log 9
u
( )
x
y
15) ln ( x ⋅ y ⋅ z 6 )
16) log 8 (w 3
3
6
)
u)
5
18) log 2 (u v )
a
17) log 7
b
Condense each expression to a single logarithm. Justify each step by stating the logarithm property used.
Level 2:
()
4
3 4
20) log 4 x − log 4 y
ln x
3
21) 2 ln a
19)
22) log 5 u − log 5 v
23) 6 log 6 7
Level 3:
24) log 5 x + log 5 y
25) 3 log 2 x − 3 log 2 y
26) 5 log u − log v
27) 3 log 7 a − 3 log 7 b
28) log 7 12 − 5 log 7 5
29) 5 log 9 6 − 5 log 9 11
Level 4:
30) log 8 x − 5 log 8 y
31) 30 log a + 6 log b
32) log 3 c +
33) log 5 z +
log 5 x
+
log 5 y
2
35) 5 log 3 x − 2 log 3 y
log 3 a
+
log 3 b
2
34) 6 ln x − 36 ln y
2
2
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36) 3 log 6 u − 18 log 6 v
Worksheet by Kuta Software LLC
ID: 2
Algebra 2 - Task 7.2
Name___________________________________
Expanding and Condensing Logarithms
Date________________ Period____
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Expand each logarithm. Justify each step by stating logarithm property used.
Level 2:
log 7 10
3
5
1) log 7 10
2) log 9 11 5 log 9 11
3
log 3 x
3
u
4) log 3 x
3) log 8
log 8 u − log 8 v
3
v
3
6) log 8 ( x ⋅ y) log 8 x + log 8 y
5) ln x 3 ln x
Level 3:
7) log 3
9) log 4
4
()
( )
x
y
7
12
4
8
8) log 4
4 log 4 8 − log 4 7
7
10) log 6 (a ⋅ b ⋅ c) log 6 a + log 6 b + log 6 c
4 log 3 x − 4 log 3 y
5
5 log 4 7 − 5 log 4 12
3
x5
11) log 5
5 log 5 x − log 5 y
y
Level 4:
12) log 6
13) log 9
( )
2 log 6 u
2
3
14) log 8 ( x ⋅ y ⋅ z
5 6
x
y
u
30 log 9 x − 6 log 9 y
15) ln ( x ⋅ y ⋅ z 6 ) ln x + ln y + 6 ln z
16) log 8 (w 3
3
18) log 2 (u v
5 4
3 4
()
6
)
log 8 x + log 8 y + 6 log 8 z
u ) 3 log 8 w +
)
log 8 u
3
3 log 2 u + 4 log 2 v
a
20 log 7 a − 4 log 7 b
b
Condense each expression to a single logarithm. Justify each step by stating the logarithm property used.
Level 2:
x
20) log 4 x − log 4 y log 4
ln x
3
19)
ln x
y
3
u
2
21) 2 ln a ln a
22) log 5 u − log 5 v log 5
v
6
23) 6 log 6 7 log 6 7
24) log 5 x + log 5 y log 5 yx
Level 3:
x3
u5
25) 3 log 2 x − 3 log 2 y log 2 33
26) 5 log u − log v log
v 12
ay
27) 3 log 7 a − 3 log 7 b log 7 3 5
28) log 7 12 − 5 log 7 5 log 7 5
x5
b6
29) 5 log 9 6 − 5 log 9 11 log 9
30)
log
x
−
5
log
y
log
8
8
8
5
5
11
y
Level 4:
17) log 7
31) 30 log a + 6 log b log (b 6 a 30 )
32) log 3 c +
log 5 x
log 5 y
log 5 (z
2
2
5
x
35) 5 log 3 x − 2 log 3 y log 3 2
y
33) log 5 z +
+
yx )
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log 3 a
+
log 3 b
2
2
x6
34) 6 ln x − 36 ln y ln 36
y
36) 3 log 6 u − 18 log 6 v log 6
log 3 (c ba )
u
3
v 18
Worksheet by Kuta Software LLC