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Math Problems
Precalculus
Quotient property of logarithms
Find the numerical value of the log expression.
\newline
log
a
=
4
log
b
=
4
log
c
=
−
4
log
a
9
b
9
c
5
\begin{array}{c} \log a=4 \quad \log b=4 \quad \log c=-4 \\ \log \frac{a^{9} b^{9}}{c^{5}} \end{array}
lo
g
a
=
4
lo
g
b
=
4
lo
g
c
=
−
4
lo
g
c
5
a
9
b
9
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log
3
(
−
cos
x
)
−
log
9
(
sin
x
)
+
1
4
=
−
log
9
2
\log _{3}(-\cos x)-\log _{9}(\sin x)+\frac{1}{4}=-\log _{9} 2
lo
g
3
(
−
cos
x
)
−
lo
g
9
(
sin
x
)
+
4
1
=
−
lo
g
9
2
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Solve for a positive value of
x
x
x
.
\newline
log
x
(
36
)
=
2
\log _{x}(36)=2
lo
g
x
(
36
)
=
2
\newline
Answer:
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Solve
(
log
81
x
)
(
1
log
x
3
)
=
6
1
4
\left(\log _{81} x\right)\left(\frac{1}{\log _{x} 3}\right)=6 \frac{1}{4}
(
lo
g
81
x
)
(
l
o
g
x
3
1
)
=
6
4
1
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(iv)
f
(
x
)
=
(
x
+
1
2
)
log
(
x
+
1
2
)
{
x
2
+
2
x
−
3
4
x
2
−
4
x
−
3
}
f(x)=\left(x+\frac{1}{2}\right) \log _{\left(x+\frac{1}{2}\right)}\left\{\frac{x^{2}+2 x-3}{4 x^{2}-4 x-3}\right\}
f
(
x
)
=
(
x
+
2
1
)
lo
g
(
x
+
2
1
)
{
4
x
2
−
4
x
−
3
x
2
+
2
x
−
3
}
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log
3
x
−
4
log
x
3
=
1
+
1
log
9
3
\log _{3} x-4 \log _{x} 3=1+\frac{1}{\log _{9} 3}
lo
g
3
x
−
4
lo
g
x
3
=
1
+
l
o
g
9
3
1
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Expand the logarithm fully using the properties of logs. Express the final answer in terms of
log
x
,
log
y
\log x, \log y
lo
g
x
,
lo
g
y
, and
log
z
\log z
lo
g
z
.
\newline
log
z
4
3
y
4
x
5
\log \frac{\sqrt[3]{z^{4}}}{y^{4} x^{5}}
lo
g
y
4
x
5
3
z
4
\newline
Answer:
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Expand the logarithm fully using the properties of logs. Express the final answer in terms of
log
x
,
log
y
\log x, \log y
lo
g
x
,
lo
g
y
, and
log
z
\log z
lo
g
z
.
\newline
log
z
x
3
y
3
\log \frac{z x^{3}}{\sqrt[3]{y}}
lo
g
3
y
z
x
3
\newline
Answer:
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Expand the logarithm fully using the properties of logs. Express the final answer in terms of
log
x
,
log
y
\log x, \log y
lo
g
x
,
lo
g
y
, and
log
z
\log z
lo
g
z
.
\newline
log
y
z
4
x
2
\log \frac{\sqrt{y} z^{4}}{x^{2}}
lo
g
x
2
y
z
4
\newline
Answer:
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Expand the logarithm fully using the properties of logs. Express the final answer in terms of
log
x
,
log
y
\log x, \log y
lo
g
x
,
lo
g
y
, and
log
z
\log z
lo
g
z
.
\newline
log
x
2
z
y
2
\log \frac{x^{2}}{\sqrt{z} y^{2}}
lo
g
z
y
2
x
2
\newline
Answer:
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Expand the logarithm fully using the properties of logs. Express the final answer in terms of
log
x
,
log
y
\log x, \log y
lo
g
x
,
lo
g
y
, and
log
z
\log z
lo
g
z
.
\newline
log
z
4
3
y
x
2
\log \frac{\sqrt[3]{z^{4}} y}{x^{2}}
lo
g
x
2
3
z
4
y
\newline
Answer:
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Expand the logarithm fully using the properties of logs. Express the final answer in terms of
log
x
,
log
y
\log x, \log y
lo
g
x
,
lo
g
y
, and
log
z
\log z
lo
g
z
.
\newline
log
x
4
y
3
z
5
\log \frac{x^{4} \sqrt{y^{3}}}{z^{5}}
lo
g
z
5
x
4
y
3
\newline
Answer:
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Expand the logarithm fully using the properties of logs. Express the final answer in terms of
log
x
,
log
y
\log x, \log y
lo
g
x
,
lo
g
y
, and
log
z
\log z
lo
g
z
.
\newline
log
z
x
2
y
4
\log \frac{z x^{2}}{y^{4}}
lo
g
y
4
z
x
2
\newline
Answer:
Get tutor help
Expand the logarithm fully using the properties of logs. Express the final answer in terms of
log
x
,
log
y
\log x, \log y
lo
g
x
,
lo
g
y
, and
log
z
\log z
lo
g
z
.
\newline
log
y
x
4
z
4
3
\log \frac{y x^{4}}{\sqrt[3]{z^{4}}}
lo
g
3
z
4
y
x
4
\newline
Answer:
Get tutor help
Expand the logarithm fully using the properties of logs. Express the final answer in terms of
log
x
,
log
y
\log x, \log y
lo
g
x
,
lo
g
y
, and
log
z
\log z
lo
g
z
.
\newline
log
x
3
z
y
2
\log \frac{\sqrt[3]{x}}{z y^{2}}
lo
g
z
y
2
3
x
\newline
Answer:
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Find the numerical value of the log expression.
\newline
log
a
=
−
10
log
b
=
11
log
c
=
4
log
c
4
a
3
b
3
\begin{array}{c} \log a=-10 \quad \log b=11 \quad \log c=4 \\ \log \frac{c^{4}}{a^{3} b^{3}} \end{array}
lo
g
a
=
−
10
lo
g
b
=
11
lo
g
c
=
4
lo
g
a
3
b
3
c
4
\newline
Answer:
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Find the numerical value of the log expression.
\newline
log
a
=
1
log
b
=
6
log
c
=
9
log
a
4
b
7
c
4
3
\begin{array}{cc} \log a=1 \quad & \log b=6 \quad \log c=9 \\ \log \frac{a^{4}}{\sqrt[3]{b^{7} c^{4}}} \end{array}
lo
g
a
=
1
lo
g
3
b
7
c
4
a
4
lo
g
b
=
6
lo
g
c
=
9
\newline
Answer:
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Find the numerical value of the log expression.
\newline
log
a
=
10
log
b
=
7
log
c
=
−
6
log
c
a
4
b
5
\begin{array}{c} \log a=10 \quad \log b=7 \quad \log c=-6 \\ \log \frac{\sqrt{c}}{a^{4} b^{5}} \end{array}
lo
g
a
=
10
lo
g
b
=
7
lo
g
c
=
−
6
lo
g
a
4
b
5
c
\newline
Answer:
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Find the numerical value of the log expression.
\newline
log
a
=
−
5
log
b
=
8
log
c
=
3
log
c
3
a
9
b
8
\begin{array}{c} \log a=-5 \quad \log b=8 \quad \log c=3 \\ \log \frac{c^{3}}{a^{9} b^{8}} \end{array}
lo
g
a
=
−
5
lo
g
b
=
8
lo
g
c
=
3
lo
g
a
9
b
8
c
3
\newline
Answer:
Get tutor help
Find the numerical value of the log expression.
\newline
log
a
=
−
8
log
b
=
9
log
c
=
−
3
log
a
9
b
9
c
8
\begin{array}{c} \log a=-8 \quad \log b=9 \quad \log c=-3 \\ \log \frac{a^{9} b^{9}}{c^{8}} \end{array}
lo
g
a
=
−
8
lo
g
b
=
9
lo
g
c
=
−
3
lo
g
c
8
a
9
b
9
\newline
Answer:
Get tutor help
Find the numerical value of the log expression.
\newline
log
a
=
−
3
log
b
=
−
11
log
c
=
8
log
a
3
b
4
c
5
\begin{array}{c} \log a=-3 \quad \log b=-11 \quad \log c=8 \\ \log \frac{\sqrt[3]{a}}{b^{4} c^{5}} \end{array}
lo
g
a
=
−
3
lo
g
b
=
−
11
lo
g
c
=
8
lo
g
b
4
c
5
3
a
\newline
Answer:
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Find the numerical value of the log expression.
\newline
log
a
=
2
log
b
=
2
log
c
=
2
log
c
7
a
9
b
5
\begin{array}{c} \log a=2 \quad \log b=2 \quad \log c=2 \\ \log \frac{c^{7}}{a^{9} b^{5}} \end{array}
lo
g
a
=
2
lo
g
b
=
2
lo
g
c
=
2
lo
g
a
9
b
5
c
7
\newline
Answer:
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Write the expression below as a single logarithm in simplest form.
\newline
2
log
b
3
−
log
b
3
2 \log _{b} 3-\log _{b} 3
2
lo
g
b
3
−
lo
g
b
3
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
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Find the numerical value of the log expression.
\newline
log
a
=
8
log
b
=
1
log
c
=
−
4
log
a
5
b
4
c
3
\begin{array}{c} \log a=8 \quad \log b=1 \quad \log c=-4 \\ \log \frac{a^{5} b^{4}}{\sqrt{c^{3}}} \end{array}
lo
g
a
=
8
lo
g
b
=
1
lo
g
c
=
−
4
lo
g
c
3
a
5
b
4
\newline
Answer:
Get tutor help
Find the numerical value of the log expression.
\newline
log
a
=
2
log
b
=
5
log
c
=
−
8
log
b
5
a
3
c
5
\begin{array}{c} \log a=2 \quad \log b=5 \quad \log c=-8 \\ \log \frac{b^{5}}{\sqrt{a^{3} c^{5}}} \end{array}
lo
g
a
=
2
lo
g
b
=
5
lo
g
c
=
−
8
lo
g
a
3
c
5
b
5
\newline
Answer:
Get tutor help
Find the numerical value of the log expression.
\newline
log
a
=
3
log
b
=
9
log
c
=
−
2
log
a
5
b
5
3
c
6
\begin{array}{c} \log a=3 \quad \log b=9 \quad \log c=-2 \\ \log \frac{\sqrt[3]{a^{5} b^{5}}}{c^{6}} \end{array}
lo
g
a
=
3
lo
g
b
=
9
lo
g
c
=
−
2
lo
g
c
6
3
a
5
b
5
\newline
Answer:
Get tutor help
Find the numerical value of the log expression.
\newline
log
a
=
9
log
b
=
6
log
c
=
4
log
b
5
c
5
a
9
\begin{array}{c} \log a=9 \quad \log b=6 \quad \log c=4 \\ \log \frac{\sqrt{b^{5} c^{5}}}{a^{9}} \end{array}
lo
g
a
=
9
lo
g
b
=
6
lo
g
c
=
4
lo
g
a
9
b
5
c
5
\newline
Answer:
Get tutor help
Find the numerical value of the log expression.
\newline
log
a
=
4
log
b
=
−
8
log
c
=
−
3
log
a
3
b
5
c
5
\begin{array}{c} \log a=4 \quad \log b=-8 \quad \log c=-3 \\ \log \frac{\sqrt{a^{3} b^{5}}}{c^{5}} \end{array}
lo
g
a
=
4
lo
g
b
=
−
8
lo
g
c
=
−
3
lo
g
c
5
a
3
b
5
\newline
Answer:
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Find the numerical value of the log expression.
\newline
log
a
=
7
log
b
=
4
log
c
=
6
log
b
8
a
6
c
5
\begin{array}{c} \log a=7 \quad \log b=4 \quad \log c=6 \\ \log \frac{b^{8}}{a^{6} c^{5}} \end{array}
lo
g
a
=
7
lo
g
b
=
4
lo
g
c
=
6
lo
g
a
6
c
5
b
8
\newline
Answer:
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Find the numerical value of the log expression.
\newline
log
a
=
12
log
b
=
12
log
c
=
−
6
log
a
2
b
9
c
5
\begin{array}{c} \log a=12 \quad \log b=12 \quad \log c=-6 \\ \log \frac{a^{2}}{b^{9} c^{5}} \end{array}
lo
g
a
=
12
lo
g
b
=
12
lo
g
c
=
−
6
lo
g
b
9
c
5
a
2
\newline
Answer:
Get tutor help
Find the numerical value of the log expression.
\newline
log
a
=
9
log
b
=
2
log
c
=
−
6
log
c
5
3
a
9
b
4
\begin{array}{c} \log a=9 \quad \log b=2 \quad \log c=-6 \\ \log \frac{\sqrt[3]{c^{5}}}{a^{9} b^{4}} \end{array}
lo
g
a
=
9
lo
g
b
=
2
lo
g
c
=
−
6
lo
g
a
9
b
4
3
c
5
\newline
Answer:
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Find the numerical value of the log expression.
\newline
log
a
=
11
log
b
=
−
7
log
c
=
−
12
log
c
3
a
9
b
6
\begin{array}{c} \log a=11 \quad \log b=-7 \quad \log c=-12 \\ \log \frac{\sqrt[3]{c}}{a^{9} b^{6}} \end{array}
lo
g
a
=
11
lo
g
b
=
−
7
lo
g
c
=
−
12
lo
g
a
9
b
6
3
c
\newline
Answer:
Get tutor help
Find the numerical value of the log expression.
\newline
log
a
=
−
6
log
b
=
10
log
c
=
7
log
b
a
5
c
7
\begin{array}{c} \log a=-6 \quad \log b=10 \quad \log c=7 \\ \log \frac{\sqrt{b}}{a^{5} c^{7}} \end{array}
lo
g
a
=
−
6
lo
g
b
=
10
lo
g
c
=
7
lo
g
a
5
c
7
b
\newline
Answer:
Get tutor help
Find the numerical value of the log expression.
\newline
log
a
=
−
6
log
b
=
−
9
log
c
=
−
12
log
b
4
c
7
3
a
4
\begin{array}{c} \log a=-6 \quad \log b=-9 \quad \log c=-12 \\ \log \frac{\sqrt[3]{b^{4} c^{7}}}{a^{4}} \end{array}
lo
g
a
=
−
6
lo
g
b
=
−
9
lo
g
c
=
−
12
lo
g
a
4
3
b
4
c
7
\newline
Answer:
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Find the numerical value of the log expression.
\newline
log
a
=
8
log
b
=
2
log
c
=
−
4
log
c
8
a
9
b
9
\begin{array}{c} \log a=8 \quad \log b=2 \quad \log c=-4 \\ \log \frac{c^{8}}{a^{9} b^{9}} \end{array}
lo
g
a
=
8
lo
g
b
=
2
lo
g
c
=
−
4
lo
g
a
9
b
9
c
8
\newline
Answer:
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Find the numerical value of the log expression.
\newline
log
a
=
−
10
log
b
=
10
log
c
=
11
log
a
b
5
c
9
\begin{array}{cc} \log a=-10 \quad & \log b=10 \quad \log c=11 \\ & \log \frac{\sqrt{a b^{5}}}{c^{9}} \end{array}
lo
g
a
=
−
10
lo
g
b
=
10
lo
g
c
=
11
lo
g
c
9
a
b
5
\newline
Answer:
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Write the expression below as a single logarithm in simplest form.
\newline
3
log
b
3
−
log
b
3
3 \log _{b} 3-\log _{b} 3
3
lo
g
b
3
−
lo
g
b
3
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
11
x
4
66
\frac{11 x^{4}}{66}
66
11
x
4
\newline
Answer:
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log
2
(
5
)
+
log
2
(
2
)
=
?
?
\log _{2}(5)+\log _{2}(2)=? ?
lo
g
2
(
5
)
+
lo
g
2
(
2
)
=
??
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Solve for the exact value of
x
x
x
.
\newline
log
3
(
6
x
)
+
log
3
(
2
)
=
3
\log _{3}(6 x)+\log _{3}(2)=3
lo
g
3
(
6
x
)
+
lo
g
3
(
2
)
=
3
\newline
Answer:
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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
7
(
5
x
)
−
3
log
7
(
2
)
=
0
\log _{7}(5 x)-3 \log _{7}(2)=0
lo
g
7
(
5
x
)
−
3
lo
g
7
(
2
)
=
0
\newline
Answer:
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Solve for the exact value of
x
x
x
.
\newline
log
4
(
8
x
)
−
log
4
(
8
)
=
3
\log _{4}(8 x)-\log _{4}(8)=3
lo
g
4
(
8
x
)
−
lo
g
4
(
8
)
=
3
\newline
Answer:
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Solve for the exact value of
x
x
x
.
\newline
log
5
(
7
x
)
+
2
log
5
(
5
)
=
4
\log _{5}(7 x)+2 \log _{5}(5)=4
lo
g
5
(
7
x
)
+
2
lo
g
5
(
5
)
=
4
\newline
Answer:
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Solve for the exact value of
x
x
x
.
\newline
log
4
(
9
x
)
−
4
log
4
(
3
)
=
0
\log _{4}(9 x)-4 \log _{4}(3)=0
lo
g
4
(
9
x
)
−
4
lo
g
4
(
3
)
=
0
\newline
Answer:
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Solve for the exact value of
x
x
x
.
\newline
log
4
(
9
x
)
+
log
4
(
9
)
=
3
\log _{4}(9 x)+\log _{4}(9)=3
lo
g
4
(
9
x
)
+
lo
g
4
(
9
)
=
3
\newline
Answer:
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Solve for the exact value of
x
x
x
.
\newline
log
2
(
9
x
)
−
log
2
(
2
)
=
5
\log _{2}(9 x)-\log _{2}(2)=5
lo
g
2
(
9
x
)
−
lo
g
2
(
2
)
=
5
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
x
729
=
6
5
\log _{x} 729=\frac{6}{5}
lo
g
x
729
=
5
6
\newline
Answer:
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Solve for the exact value of
x
x
x
.
\newline
log
4
(
3
x
)
−
2
log
4
(
2
)
=
2
\log _{4}(3 x)-2 \log _{4}(2)=2
lo
g
4
(
3
x
)
−
2
lo
g
4
(
2
)
=
2
\newline
Answer:
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Solve for the exact value of
x
x
x
.
\newline
log
4
(
2
x
)
−
3
log
4
(
9
)
=
0
\log _{4}(2 x)-3 \log _{4}(9)=0
lo
g
4
(
2
x
)
−
3
lo
g
4
(
9
)
=
0
\newline
Answer:
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