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Math Problems
Precalculus
Product property of logarithms
Evaluate.
\newline
log
8
512
5
\log _{8} \sqrt[5]{512}
lo
g
8
5
512
\newline
Write your answer in simplest form.
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Evaluate:
\newline
log
8
4
\log _{8} 4
lo
g
8
4
\newline
Answer:
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Evaluate:
\newline
log
64
16
\log _{64} 16
lo
g
64
16
\newline
Answer:
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Evaluate:
\newline
log
125
25
\log _{125} 25
lo
g
125
25
\newline
Answer:
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Evaluate:
\newline
log
125
5
\log _{125} 5
lo
g
125
5
\newline
Answer:
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Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
log
12
(
1
2
4
z
)
\log _{12}\left(12^{4 z}\right)
lo
g
12
(
1
2
4
z
)
\newline
Answer:
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Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
log
3
(
3
3
y
3
)
\log _{3}\left(3^{3 y^{3}}\right)
lo
g
3
(
3
3
y
3
)
\newline
Answer:
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Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
log
8
(
8
2
y
2
)
\log _{8}\left(8^{2 y^{2}}\right)
lo
g
8
(
8
2
y
2
)
\newline
Answer:
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Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
(
4
log
4
(
4
z
)
)
\left(4^{\log _{4}(4 \sqrt{z})}\right)
(
4
l
o
g
4
(
4
z
)
)
\newline
Answer:
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Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
log
6
(
6
3
z
3
)
\log _{6}\left(6^{3 z^{3}}\right)
lo
g
6
(
6
3
z
3
)
\newline
Answer:
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Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
log
7
(
7
w
2
)
\log _{7}\left(7^{w^{2}}\right)
lo
g
7
(
7
w
2
)
\newline
Answer:
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Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
log
6
(
6
8
w
2
)
\log _{6}\left(6^{8 w^{2}}\right)
lo
g
6
(
6
8
w
2
)
\newline
Answer:
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92
92
92
)
log
30
=
log
(
−
3
b
−
5
)
\log 30=\log (-3 b-5)
lo
g
30
=
lo
g
(
−
3
b
−
5
)
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Use a calculator.
\newline
Find
log
7
1
\log_{7}1
lo
g
7
1
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Expand the logarithm. Assume all expressions exist and are well-defined.
\newline
Write your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.
\newline
log
(
v
w
u
)
\log(vwu)
lo
g
(
v
w
u
)
\newline
______
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