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Math Problems
Precalculus
Product property of logarithms
Rewrite as a quotient of two common logarithms. Write your answer in simplest form.
log
3
33
=
\log_3 33 =
lo
g
3
33
=
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What is the domain of this logarithmic function?
y
=
log
8
(
x
−
5
)
+
3
\newline y=\log_8(x-5)+3\newline
y
=
lo
g
8
(
x
−
5
)
+
3
Express the domain in inequality notation.
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What is the domain of this logarithmic function?
y
=
log
4
(
x
+
5
)
−
2
\newline y=\log_4(x+5)-2\newline
y
=
lo
g
4
(
x
+
5
)
−
2
Express the domain in inequality notation.
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Solve for
p
p
p
.
\newline
3
log
2
(
p
+
4
)
=
9
3 \, \log_2(p+4)=9
3
lo
g
2
(
p
+
4
)
=
9
.
\newline
Write your answer in simplest form.
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Solve for
x
x
x
.
\newline
log
4
x
=
2
\log_4 x = 2
lo
g
4
x
=
2
\newline
Write your answer in simplest form.
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log
10
\log 10
lo
g
10
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Evaluate:
log
4
(
8
−
x
)
=
log
4
(
6
)
\log_{4}(8-x)=\log_{4}(6)
lo
g
4
(
8
−
x
)
=
lo
g
4
(
6
)
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Simplify the following:
\newline
log
3
(
2
x
)
+
log
3
w
\log _{3}(2 x)+\log _{3} w
lo
g
3
(
2
x
)
+
lo
g
3
w
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Without the use of calculators or software establish which number is larger:
\newline
log
189
1323
\log_{189}1323
lo
g
189
1323
or
log
63
147
\log_{63}147
lo
g
63
147
.
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Use the laws of logarithms to solve
\newline
log
2
(
16
x
)
+
log
2
(
x
+
1
)
=
3
+
log
2
(
x
+
6
)
\log_{2}(16x)+\log_{2}(x+1)=3+\log_{2}(x+6)
lo
g
2
(
16
x
)
+
lo
g
2
(
x
+
1
)
=
3
+
lo
g
2
(
x
+
6
)
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Solve for a positive value of
x
x
x
.
\newline
log
3
(
729
)
=
x
\log _{3}(729)=x
lo
g
3
(
729
)
=
x
\newline
Answer:
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Solve for a positive value of
x
x
x
.
\newline
log
5
(
x
)
=
2
\log _{5}(x)=2
lo
g
5
(
x
)
=
2
\newline
Answer:
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Solve for a positive value of
x
x
x
.
\newline
log
x
(
4
)
=
2
\log _{x}(4)=2
lo
g
x
(
4
)
=
2
\newline
Answer:
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Solve for a positive value of
x
x
x
.
\newline
log
2
(
x
)
=
7
\log _{2}(x)=7
lo
g
2
(
x
)
=
7
\newline
Answer:
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Solve for a positive value of
x
x
x
.
\newline
log
x
(
216
)
=
3
\log _{x}(216)=3
lo
g
x
(
216
)
=
3
\newline
Answer:
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Solve for a positive value of
x
x
x
.
\newline
log
9
(
x
)
=
3
\log _{9}(x)=3
lo
g
9
(
x
)
=
3
\newline
Answer:
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Solve for a positive value of
x
x
x
.
\newline
log
2
(
64
)
=
x
\log _{2}(64)=x
lo
g
2
(
64
)
=
x
\newline
Answer:
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Solve for a positive value of
x
x
x
.
\newline
log
8
(
64
)
=
x
\log _{8}(64)=x
lo
g
8
(
64
)
=
x
\newline
Answer:
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Solve for a positive value of
x
x
x
.
\newline
log
2
(
x
)
=
9
\log _{2}(x)=9
lo
g
2
(
x
)
=
9
\newline
Answer:
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Solve for a positive value of
x
x
x
.
\newline
log
8
(
512
)
=
x
\log _{8}(512)=x
lo
g
8
(
512
)
=
x
\newline
Answer:
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Solve for a positive value of
x
x
x
.
\newline
log
5
(
x
)
=
4
\log _{5}(x)=4
lo
g
5
(
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
.
\newline
log
4
x
3
\log 4 x^{3}
lo
g
4
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 x
lo
g
x
.
\newline
log
6
x
4
\log 6 x^{4}
lo
g
6
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
.
\newline
log
5
x
2
\log 5 x^{2}
lo
g
5
x
2
\newline
Answer:
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Condense the logarithm
\newline
q
log
b
−
z
log
k
q \log b-z \log k
q
lo
g
b
−
z
lo
g
k
\newline
Answer:
log
(
□
)
\log (\square)
lo
g
(
□
)
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Solve for the exact value of
x
x
x
.
\newline
log
5
(
4
x
)
−
2
log
5
(
4
)
=
1
\log _{5}(4 x)-2 \log _{5}(4)=1
lo
g
5
(
4
x
)
−
2
lo
g
5
(
4
)
=
1
\newline
Answer:
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Solve for the exact value of
x
x
x
.
\newline
log
5
(
5
x
)
+
log
5
(
2
)
=
0
\log _{5}(5 x)+\log _{5}(2)=0
lo
g
5
(
5
x
)
+
lo
g
5
(
2
)
=
0
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
x
216
=
3
\log _{x} 216=3
lo
g
x
216
=
3
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
2
x
=
−
5
\log _{2} x=-5
lo
g
2
x
=
−
5
\newline
Answer:
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Solve the following logarithm problem for the positive solution for
x
x
x
.
\newline
log
6
x
=
−
3
\log _{6} x=-3
lo
g
6
x
=
−
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
(
2
)
=
4
x
\log (2)=4 x
lo
g
(
2
)
=
4
x
\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
(
3
)
=
3
\log _{3 x}(3)=3
lo
g
3
x
(
3
)
=
3
\newline
Answer:
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Solve the following for `x`
\newline
log
(
2
x
)
−
log
(
x
−
3
)
=
1
\log(2x)-\log(x-3)=1
lo
g
(
2
x
)
−
lo
g
(
x
−
3
)
=
1
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Evaluate each expression.
\newline
log
7
343
\log_{7}343
lo
g
7
343
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What is the value of
log
5
1
\log_{5}1
lo
g
5
1
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rewrite the following in the form
log
(
c
)
\log(c)
lo
g
(
c
)
log
(
3
)
+
log
(
4
)
\log(3) + \log(4)
lo
g
(
3
)
+
lo
g
(
4
)
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Evaluate.
\newline
log
6
216
5
\log _{6} \sqrt[5]{216}
lo
g
6
5
216
\newline
Write your answer in simplest form.
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What is the value of
log
4
1
\log _{4} 1
lo
g
4
1
?
\newline
Answer:
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What is the value of
log
2
1
\log _{2} 1
lo
g
2
1
?
\newline
Answer:
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What is the value of
log
7
1
\log _{7} 1
lo
g
7
1
?
\newline
Answer:
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Evaluate.
\newline
log
4
4
5
\log _{4} \sqrt[5]{4}
lo
g
4
5
4
\newline
Write your answer in simplest form.
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What is the value of
log
5
1
\log _{5} 1
lo
g
5
1
?
\newline
Answer:
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What is the value of
log
6
1
\log _{6} 1
lo
g
6
1
?
\newline
Answer:
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What is the value of
log
4
4
\log _{4} 4
lo
g
4
4
?
\newline
Answer:
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Evaluate.
\newline
log
4
64
\log _{4} 64
lo
g
4
64
\newline
Write your answer in simplest form.
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Evaluate.
\newline
log
3
243
\log _{3} 243
lo
g
3
243
\newline
Write your answer in simplest form.
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Evaluate.
\newline
log
6
216
\log _{6} 216
lo
g
6
216
\newline
Write your answer in simplest form.
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Evalute.
\newline
log
7
49
\log _{7} 49
lo
g
7
49
\newline
Write your answer in simplest form.
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What is the value of
log
2
4
\log _{2} 4
lo
g
2
4
?
\newline
Answer:
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What is the value of
log
9
1
\log _{9} 1
lo
g
9
1
?
\newline
Answer:
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