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Let’s check out your problem:
Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
log
11
(
1
1
−
5
z
3
)
\log _{11}\left(11^{-5 z^{3}}\right)
lo
g
11
(
1
1
−
5
z
3
)
\newline
Answer:
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Math Problems
Precalculus
Quotient property of logarithms
Full solution
Q.
Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
log
11
(
1
1
−
5
z
3
)
\log _{11}\left(11^{-5 z^{3}}\right)
lo
g
11
(
1
1
−
5
z
3
)
\newline
Answer:
Apply Inverse Property:
Let's apply the inverse property of logarithms which states that
log
b
b
x
=
x
\log_b b^{x} = x
lo
g
b
b
x
=
x
.
log
11
(
1
1
−
5
z
3
)
=
−
5
z
3
\log_{11}(11^{-5z^{3}}) = -5z^{3}
lo
g
11
(
1
1
−
5
z
3
)
=
−
5
z
3
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Question
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\newline
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\newline
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