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Math Problems
Precalculus
Quotient property of logarithms
Solve for the exact value of
x
x
x
.
\newline
log
4
(
5
x
)
+
log
4
(
7
)
=
3
\log _{4}(5 x)+\log _{4}(7)=3
lo
g
4
(
5
x
)
+
lo
g
4
(
7
)
=
3
\newline
Answer:
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Solve for the exact value of
x
x
x
.
\newline
log
6
(
4
x
)
+
log
6
(
9
)
=
3
\log _{6}(4 x)+\log _{6}(9)=3
lo
g
6
(
4
x
)
+
lo
g
6
(
9
)
=
3
\newline
Answer:
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Write the log equation as an exponential equation. You do not need to solve for
x
\mathrm{x}
x
.
\newline
log
4
x
(
4
x
)
=
9
8
\log _{4 x}(4 x)=\frac{9}{8}
lo
g
4
x
(
4
x
)
=
8
9
\newline
Answer:
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Write the log equation as an exponential equation. You do not need to solve for
x
\mathrm{x}
x
.
\newline
log
3
x
(
4
x
)
=
4
9
\log _{3 x}(4 x)=\frac{4}{9}
lo
g
3
x
(
4
x
)
=
9
4
\newline
Answer:
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Write the log equation as an exponential equation. You do not need to solve for
x
\mathrm{x}
x
.
\newline
log
2
x
(
2
)
=
5
3
\log _{2 x}(2)=\frac{5}{3}
lo
g
2
x
(
2
)
=
3
5
\newline
Answer:
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Write the log equation as an exponential equation. You do not need to solve for
x
\mathrm{x}
x
.
\newline
log
(
x
+
5
)
(
2
x
)
=
6
7
\log _{(x+5)}(2 x)=\frac{6}{7}
lo
g
(
x
+
5
)
(
2
x
)
=
7
6
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
9
x
=
−
1
2
\log _{9} x=-\frac{1}{2}
lo
g
9
x
=
−
2
1
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
16
x
=
−
5
4
\log _{16} x=-\frac{5}{4}
lo
g
16
x
=
−
4
5
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
100
x
=
−
1
2
\log _{100} x=-\frac{1}{2}
lo
g
100
x
=
−
2
1
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
x
216
=
3
2
\log _{x} 216=\frac{3}{2}
lo
g
x
216
=
2
3
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
64
x
=
−
1
3
\log _{64} x=-\frac{1}{3}
lo
g
64
x
=
−
3
1
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
x
25
=
2
3
\log _{x} 25=\frac{2}{3}
lo
g
x
25
=
3
2
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
x
5
=
1
2
\log _{x} 5=\frac{1}{2}
lo
g
x
5
=
2
1
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
16
x
=
−
1
2
\log _{16} x=-\frac{1}{2}
lo
g
16
x
=
−
2
1
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
x
343
=
3
2
\log _{x} 343=\frac{3}{2}
lo
g
x
343
=
2
3
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
x
64
=
6
5
\log _{x} 64=\frac{6}{5}
lo
g
x
64
=
5
6
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
x
1
8
=
−
3
4
\log _{x} \frac{1}{8}=-\frac{3}{4}
lo
g
x
8
1
=
−
4
3
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
27
x
=
−
2
3
\log _{27} x=-\frac{2}{3}
lo
g
27
x
=
−
3
2
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
25
x
=
1
2
\log _{25} x=\frac{1}{2}
lo
g
25
x
=
2
1
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
16
x
=
1
2
\log _{16} x=\frac{1}{2}
lo
g
16
x
=
2
1
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
x
10
=
1
3
\log _{x} 10=\frac{1}{3}
lo
g
x
10
=
3
1
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
125
x
=
−
4
3
\log _{125} x=-\frac{4}{3}
lo
g
125
x
=
−
3
4
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
x
1
4
=
−
2
5
\log _{x} \frac{1}{4}=-\frac{2}{5}
lo
g
x
4
1
=
−
5
2
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
125
x
=
2
3
\log _{125} x=\frac{2}{3}
lo
g
125
x
=
3
2
\newline
Answer:
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Evaluate.
\newline
log
7
1
4
\log _{7} \frac{1}{4}
lo
g
7
4
1
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Solve the following for
x
x
x
.
\newline
log
3
(
x
2
−
24
)
=
log
3
(
5
x
)
\log_{3}(x^{2}-24)=\log_{3}(5x)
lo
g
3
(
x
2
−
24
)
=
lo
g
3
(
5
x
)
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log
9
5
+
log
9
8
=
\log_{9}5+\log_{9}8=
lo
g
9
5
+
lo
g
9
8
=
Get tutor help
Evaluate:
\newline
log
25
(
1
125
)
\log_{25}\left(\frac{1}{125}\right)
lo
g
25
(
125
1
)
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Select the answer which is equivalent to the given expression using your calculator.
\newline
log
49
343
\log _{49} 343
lo
g
49
343
\newline
3
2
\frac{3}{2}
2
3
\newline
2
5
\frac{2}{5}
5
2
\newline
2
3
\frac{2}{3}
3
2
\newline
5
2
\frac{5}{2}
2
5
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Evaluate.
\newline
log
5
1
5
\log _{5} \frac{1}{5}
lo
g
5
5
1
\newline
Write your answer in simplest form.
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Evaluate:
\newline
log
27
1
9
\log _{27} \frac{1}{9}
lo
g
27
9
1
\newline
Answer:
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Evaluate:
\newline
log
32
1
64
\log _{32} \frac{1}{64}
lo
g
32
64
1
\newline
Answer:
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Evaluate:
\newline
log
125
1
25
\log _{125} \frac{1}{25}
lo
g
125
25
1
\newline
Answer:
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Evaluate:
\newline
log
16
1
64
\log _{16} \frac{1}{64}
lo
g
16
64
1
\newline
Answer:
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Evaluate:
\newline
log
9
1
3
\log _{9} \frac{1}{3}
lo
g
9
3
1
\newline
Answer:
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Evaluate:
\newline
log
4
1
8
\log _{4} \frac{1}{8}
lo
g
4
8
1
\newline
Answer:
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Evaluate:
\newline
log
243
1
9
\log _{243} \frac{1}{9}
lo
g
243
9
1
\newline
Answer:
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Evaluate:
\newline
log
25
1
125
\log _{25} \frac{1}{125}
lo
g
25
125
1
\newline
Answer:
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Evaluate.
\newline
log
3
1
81
\log _{3} \frac{1}{81}
lo
g
3
81
1
\newline
Write your answer in simplest form.
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Evaluate.
\newline
log
1
100
\log \frac{1}{100}
lo
g
100
1
\newline
Write your answer in simplest form.
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Evaluate:
\newline
log
32
1
8
\log _{32} \frac{1}{8}
lo
g
32
8
1
\newline
Answer:
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Evaluate:
\newline
log
64
1
4
\log _{64} \frac{1}{4}
lo
g
64
4
1
\newline
Answer:
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Evaluate:
\newline
log
81
1
243
\log _{81} \frac{1}{243}
lo
g
81
243
1
\newline
Answer:
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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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Express the given expression as an integer or as a fraction in simplest form.
\newline
log
3
(
3
1
2
)
\log _{3}\left(3^{\frac{1}{2}}\right)
lo
g
3
(
3
2
1
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
log
3
(
1
3
7
)
\log _{3}\left(\frac{1}{3^{7}}\right)
lo
g
3
(
3
7
1
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
log
3
(
1
3
)
\log _{3}\left(\frac{1}{\sqrt{3}}\right)
lo
g
3
(
3
1
)
\newline
Answer:
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log
(
16
)
log
(
4
)
\frac{\log(16)}{\log(4)}
l
o
g
(
4
)
l
o
g
(
16
)
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y
=
log
2
(
x
+
2
)
+
2
y=\log _{2}(x+2)+2
y
=
lo
g
2
(
x
+
2
)
+
2
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Find the
11
11
11
values of
x
x
x
.
\newline
log
2
(
x
+
2
)
+
log
2
(
x
+
6
)
=
5
\log_{2}(x+2)+\log_{2}(x+6)=5
lo
g
2
(
x
+
2
)
+
lo
g
2
(
x
+
6
)
=
5
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