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Math Problems
Algebra 2
Product property of logarithms
Evaluate the logarithm.
\newline
Round your answer to the nearest thousandth.
\newline
log
4
(
1
19
)
≈
\log _{4}\left(\frac{1}{19}\right) \approx
lo
g
4
(
19
1
)
≈
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Evaluate the logarithm.
\newline
Round your answer to the nearest thousandth.
\newline
log
2
(
1
50
)
≈
\log _{2}\left(\frac{1}{50}\right) \approx
lo
g
2
(
50
1
)
≈
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4
⋅
5
−
6
t
=
2000
4 \cdot 5^{-6 t}=2000
4
⋅
5
−
6
t
=
2000
\newline
Which of the following is the solution of the equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
t
=
−
log
5
(
500
)
6
t=\frac{-\log _{5}(500)}{6}
t
=
6
−
l
o
g
5
(
500
)
\newline
(B)
t
=
−
log
20
(
2000
)
6
t=\frac{-\log _{20}(2000)}{6}
t
=
6
−
l
o
g
20
(
2000
)
\newline
(C)
t
=
−
log
2000
(
20
)
6
t=\frac{-\log _{2000}(20)}{6}
t
=
6
−
l
o
g
2000
(
20
)
\newline
(D)
t
=
−
log
500
(
5
)
6
t=\frac{-\log _{500}(5)}{6}
t
=
6
−
l
o
g
500
(
5
)
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Which of the following is equivalent to
log
2
(
c
)
⋅
log
c
(
2
)
\log _{2}(c) \cdot \log _{c}(2)
lo
g
2
(
c
)
⋅
lo
g
c
(
2
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
log
(
c
)
\log (c)
lo
g
(
c
)
\newline
(B)
log
(
2
)
\log (2)
lo
g
(
2
)
\newline
(C)
1
1
1
\newline
(D)
−
1
-1
−
1
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Which of the following is equivalent to
log
c
(
16
)
⋅
log
2
(
c
)
\log _{c}(16) \cdot \log _{2}(c)
lo
g
c
(
16
)
⋅
lo
g
2
(
c
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
4
4
\newline
(B)
8
8
8
\newline
(C)
log
(
8
)
\log (8)
lo
g
(
8
)
\newline
(D)
log
c
(
4
)
\log _{c}(4)
lo
g
c
(
4
)
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Which of the following is equivalent to
log
3
(
b
)
⋅
log
b
(
27
)
\log _{3}(b) \cdot \log _{b}(27)
lo
g
3
(
b
)
⋅
lo
g
b
(
27
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
3
3
\newline
(B)
9
9
9
\newline
(C)
log
(
9
)
\log (9)
lo
g
(
9
)
\newline
(D)
log
b
(
3
)
\log _{b}(3)
lo
g
b
(
3
)
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Which of the following is equivalent to
log
4
(
m
)
⋅
log
m
(
20
)
\log _{4}(m) \cdot \log _{m}(20)
lo
g
4
(
m
)
⋅
lo
g
m
(
20
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
5
5
5
\newline
(B)
80
80
80
\newline
(C)
log
(
5
)
\log (5)
lo
g
(
5
)
\newline
(D)
log
4
(
20
)
\log _{4}(20)
lo
g
4
(
20
)
Get tutor help
Which of the following is equivalent to
log
9
(
m
)
log
(
m
)
\frac{\log _{9}(m)}{\log (m)}
l
o
g
(
m
)
l
o
g
9
(
m
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
log
(
9
)
\log (9)
lo
g
(
9
)
\newline
(B)
log
9
(
1
)
\log _{9}(1)
lo
g
9
(
1
)
\newline
(C)
1
log
(
m
)
\frac{1}{\log (m)}
l
o
g
(
m
)
1
\newline
(D)
1
log
(
9
)
\frac{1}{\log (9)}
l
o
g
(
9
)
1
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Which of the following is equivalent to
log
(
a
)
⋅
log
a
(
5
)
\log (a) \cdot \log _{a}(5)
lo
g
(
a
)
⋅
lo
g
a
(
5
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
log
(
a
)
\log (a)
lo
g
(
a
)
\newline
(B)
log
(
5
)
\log (5)
lo
g
(
5
)
\newline
(C)
log
(
5
a
)
\log (5 a)
lo
g
(
5
a
)
\newline
(D)
log
a
(
5
a
)
\log _{a}(5 a)
lo
g
a
(
5
a
)
Get tutor help
Which of the following is equivalent to
log
7
(
a
)
⋅
log
b
(
7
)
\log _{7}(a) \cdot \log _{b}(7)
lo
g
7
(
a
)
⋅
lo
g
b
(
7
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
log
(
7
)
\log (7)
lo
g
(
7
)
\newline
(B)
log
(
7
a
)
\log (7 a)
lo
g
(
7
a
)
\newline
(C)
log
a
(
b
)
\log _{a}(b)
lo
g
a
(
b
)
\newline
(D)
log
b
(
a
)
\log _{b}(a)
lo
g
b
(
a
)
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Which of the following is equivalent to
log
a
(
18
)
⋅
log
3
(
a
)
\log _{a}(18) \cdot \log _{3}(a)
lo
g
a
(
18
)
⋅
lo
g
3
(
a
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
6
6
6
\newline
(B)
log
(
6
)
\log (6)
lo
g
(
6
)
\newline
(C)
log
3
(
18
)
\log _{3}(18)
lo
g
3
(
18
)
\newline
(D)
log
18
(
3
)
\log _{18}(3)
lo
g
18
(
3
)
Get tutor help
Which of the following is equivalent to
log
(
t
)
log
8
(
t
)
\frac{\log (t)}{\log _{8}(t)}
l
o
g
8
(
t
)
l
o
g
(
t
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
log
(
8
)
\log (8)
lo
g
(
8
)
\newline
(B)
log
8
(
t
2
)
\log _{8}\left(t^{2}\right)
lo
g
8
(
t
2
)
\newline
(C)
1
log
(
8
)
\frac{1}{\log (8)}
l
o
g
(
8
)
1
\newline
(D)
1
log
8
(
t
2
)
\frac{1}{\log _{8}\left(t^{2}\right)}
l
o
g
8
(
t
2
)
1
Get tutor help
Which of the following is equivalent to
log
b
(
8
)
log
b
(
2
)
\frac{\log _{b}(8)}{\log _{b}(2)}
l
o
g
b
(
2
)
l
o
g
b
(
8
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
3
3
\newline
(B)
4
4
4
\newline
(C)
log
b
(
3
)
\log _{b}(3)
lo
g
b
(
3
)
\newline
(D)
log
(
4
)
\log (4)
lo
g
(
4
)
Get tutor help
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
(
u
v
)
\log(uv)
lo
g
(
uv
)
\newline
_____
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