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Math Problems
Precalculus
Power property of logarithms
Add, subtract, multiply, or divide as indicated to simplify each expression. Remember to work within the parentheses first.
\newline
12
÷
(
6
÷
2
)
12\div(6\div2)
12
÷
(
6
÷
2
)
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Expand the logarithm fully using the properties of logs. Express the final answer in terms of
log
x
\log x
lo
g
x
, and
log
y
\log y
lo
g
y
.
\newline
log
x
5
y
2
\log x^{5} y^{2}
lo
g
x
5
y
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 x
lo
g
x
.
\newline
log
8
x
4
\log 8 x^{4}
lo
g
8
x
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 x
lo
g
x
, and
log
y
\log y
lo
g
y
.
\newline
log
x
3
y
4
\log x^{3} y^{4}
lo
g
x
3
y
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 x
lo
g
x
, and
log
y
\log y
lo
g
y
.
\newline
log
x
5
y
\log x^{5} y
lo
g
x
5
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 x
lo
g
x
, and
log
y
\log y
lo
g
y
.
\newline
log
x
3
y
\log x^{3} y
lo
g
x
3
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 x
lo
g
x
, and
log
y
\log y
lo
g
y
.
\newline
log
x
2
y
4
\log x^{2} y^{4}
lo
g
x
2
y
4
\newline
Answer:
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Condense the logarithm
\newline
log
c
+
x
log
d
\log c+x \log d
lo
g
c
+
x
lo
g
d
\newline
Answer:
log
(
□
)
\log (\square)
lo
g
(
□
)
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what is the integral of
x
2
log
(
x
)
\frac{x^2}{\log(x)}
l
o
g
(
x
)
x
2
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Integrate
∫
cos
3
x
d
x
\int \cos ^{3} x d x
∫
cos
3
x
d
x
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∫
sin
5
x
cos
5
x
d
x
\int \sin ^{5} x \cos ^{5} x d x
∫
sin
5
x
cos
5
x
d
x
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Write in exponential notation:
\newline
(
2
a
2
)
4
(2a^{2})^{4}
(
2
a
2
)
4
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Write in exponential notation:
\newline
(
3
a
2
b
)
4
(3a^{2}b)^{4}
(
3
a
2
b
)
4
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∫
sin
3
x
d
x
\int \sin ^{3} x d x
∫
sin
3
x
d
x
=
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What is the value of
log
10
\log \sqrt{10}
lo
g
10
?
\newline
Answer:
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Evaluate.
\newline
log
8
512
4
\log _{8} \sqrt[4]{512}
lo
g
8
4
512
\newline
Write your answer in simplest form.
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Write in standard form:
\newline
5
×
1
0
1
5 \times 10^{1}
5
×
1
0
1
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Write in standard form:
\newline
2
×
1
0
6
2 \times 10^{6}
2
×
1
0
6
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Write in standard form:
\newline
3
×
1
0
2
3 \times 10^{2}
3
×
1
0
2
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Write in standard form:
\newline
7
×
1
0
0
7 \times 10^{0}
7
×
1
0
0
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Expand each logarithm
\newline
71
71
71
)
log
x
3
\log x^{3}
lo
g
x
3
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∫
x
2
d
x
\int x^{2}dx
∫
x
2
d
x
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∫
sin
2
x
cos
2
x
d
x
\int \sin^{2}x \cos^{2}x \, dx
∫
sin
2
x
cos
2
x
d
x
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what is
log
(
10
)
\log(10)
lo
g
(
10
)
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∫
e
5
x
d
x
\int e^{5x} \, dx
∫
e
5
x
d
x
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∫
3
x
2
5
d
x
\int 3\sqrt[5]{x^{2}}\,dx
∫
3
5
x
2
d
x
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Simplify
e
2
ln
4
−
3
e^{2 \ln 4-3}
e
2
l
n
4
−
3
and write without any logarithms.
\newline
Answer:
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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
(
w
2
)
\log(w^2)
lo
g
(
w
2
)
\newline
_____
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