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Math Problems
Precalculus
Properties of logarithms: mixed review
Consider the equation
0.75
⋅
1
0
w
3
=
30
0.75 \cdot 10^{\frac{w}{3}}=30
0.75
⋅
1
0
3
w
=
30
.
\newline
Solve the equation for
w
w
w
. Express the solution as a logarithm in base
−
10
-10
−
10
.
\newline
w
=
w=
w
=
\newline
□
\square
□
\newline
Approximate the value of
w
w
w
. Round your answer to the nearest thousandth.
\newline
w
≈
w \approx
w
≈
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1
1
1
. Find the value of
log
5
\log _{5}
lo
g
5
\qquad
(AHSME
1950
1950
1950
)
\newline
2
2
2
. What is the logarithm of
27
9
4
9
3
27 \sqrt[4]{9} \sqrt[3]{9}
27
4
9
3
9
base
3
3
3
? (AHSME
1953
1953
1953
)
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vert Log Equation to Exponential
\newline
This is the only question in this section.
\newline
uestion
\newline
Vrite the log equation as an exponential equation. Yor
\newline
log
5
x
(
x
+
1
)
=
8
3
\log _{5 x}(x+1)=\frac{8}{3}
lo
g
5
x
(
x
+
1
)
=
3
8
\newline
Answer Aftempt
2
2
2
out of
2
2
2
\newline
5
x
8
3
=
x
+
1
5 x^{\frac{8}{3}}=x+1
5
x
3
8
=
x
+
1
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4
4
4
. Use the Change of Base Formula to evaluate
log
5
92
\log _{5} 92
lo
g
5
92
. Then convert
log
5
92
\log _{5} 92
lo
g
5
92
to a logarithm in base
3
3
3
. Round to the nearest thousandth.
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log
2
(
4
x
−
3
)
+
log
2
(
3
x
+
5
)
=
\log _{2}(4 x-3)+\log _{2}(3 x+5)=
lo
g
2
(
4
x
−
3
)
+
lo
g
2
(
3
x
+
5
)
=
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Simplify:
2
(
4
x
−
5
)
−
3
(
x
−
1
)
+
x
2(4 x-5)-3(x-1)+x
2
(
4
x
−
5
)
−
3
(
x
−
1
)
+
x
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Write in exponential notation:
\newline
(
4
n
−
3
)
2
(4n^{-3})^{2}
(
4
n
−
3
)
2
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7
log
c
(
w
−
7
)
−
3
log
c
(
w
+
2
)
7\log_{c}(w-7)-3\log_{c}(w+2)
7
lo
g
c
(
w
−
7
)
−
3
lo
g
c
(
w
+
2
)
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Exponential and Logarithmic Functions Writing an expression as a single logarithm
\newline
Write the expression as a single logarithm.
\newline
7
log
c
(
w
−
7
)
−
3
log
c
(
w
+
2
)
7 \log _{c}(w-7)-3 \log _{c}(w+2)
7
lo
g
c
(
w
−
7
)
−
3
lo
g
c
(
w
+
2
)
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Consider the equation
\newline
−
5
e
10
t
=
−
30
-5e^{10t} = -30
−
5
e
10
t
=
−
30
. Solve the equation for
t
t
t
. Express the solution as a logarithm in base-
e
e
e
.
\newline
t
=
t=
t
=
\newline
Approximate the value of
t
t
t
. Round your answer to the nearest thousandth.
\newline
t
≈
t \approx
t
≈
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log
(
10
×
x
−
3
)
\log(10 \times\sqrt{x-3})
lo
g
(
10
×
x
−
3
)
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