Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Algebra 2
Quotient property of logarithms
Use the quotient property of logs to write as a difference of logarithms. Simplify if possible.
\newline
log
(
100
y
)
\log\left(\frac{100}{y}\right)
lo
g
(
y
100
)
\newline
Show your work here
\newline
Hint: To add a logarithm, type "log"
Get tutor help
log
a
12
+
log
a
27
log
a
18
\frac{\log _{a} 12+\log _{a} 27}{\log _{a} 18}
l
o
g
a
18
l
o
g
a
12
+
l
o
g
a
27
Get tutor help
d) If
log
10
y
=
2
3
log
10
x
−
2
\log _{10} y=\frac{2}{3} \log _{10} x-2
lo
g
10
y
=
3
2
lo
g
10
x
−
2
, express
y
y
y
in terms of
x
x
x
with no logarithmic expression.
\newline
2
2
2
Get tutor help
a)
1
3
log
(
x
)
+
log
(
3
)
=
log
(
5
)
\frac{1}{3} \log (x)+\log (3)=\log (5)
3
1
lo
g
(
x
)
+
lo
g
(
3
)
=
lo
g
(
5
)
.
Get tutor help
3
3
3
.) Find the value of
x
x
x
and
y
y
y
\newline
17
x
−
70
∣
(
3
x
+
5
2
x
+
5
)
17x-70|\left(\frac{3x+5}{2x+5}\right)
17
x
−
70∣
(
2
x
+
5
3
x
+
5
)
Get tutor help
M
⋅
V
=
P
⋅
Q
M \cdot V=P \cdot Q
M
⋅
V
=
P
⋅
Q
\newline
The quantitative theory of money states that given
M
M
M
dollars in circulation in a year, a monetary velocity of
V
V
V
, a price level of
P
P
P
, and a real output of
Q
Q
Q
dollars, the given equation is correct. An economist considers the case where the dollars in circulation and the real output are known constants. Which of the following expressions is the change in monetary velocity as the price level increases by
1
1
1
?
\newline
Choose
1
1
1
answer:
\newline
(A)
M
M
M
\newline
(B)
Q
Q
Q
\newline
(C)
M
Q
\frac{M}{Q}
Q
M
\newline
(D)
Q
M
\frac{Q}{M}
M
Q
Get tutor help
5
k
−
2
−
2
k
−
2
k
−
1
=
−
1
\frac{5}{k-2}-\frac{2 k-2}{k-1}=-1
k
−
2
5
−
k
−
1
2
k
−
2
=
−
1
\newline
What is the sum of all the possible values for
k
k
k
that satisfy the given equation?
\newline
□
\square
□
Get tutor help
4
y
2
+
9
=
6
x
+
3
4
y
=
2
x
+
1
\begin{array}{r} 4 y^{2}+9=6 x+3 \\ 4 y=2 x+1 \end{array}
4
y
2
+
9
=
6
x
+
3
4
y
=
2
x
+
1
\newline
If
(
x
,
y
)
(x, y)
(
x
,
y
)
is the solution to the system of equations shown, what is the value of
y
y
y
?
\newline
□
\square
□
Get tutor help
What is the inverse of the function
y
=
log
3
x
y=\log _{3} x
y
=
lo
g
3
x
?
\newline
(
1
1
1
)
y
=
x
3
y=x^{3}
y
=
x
3
\newline
(
3
3
3
)
y
=
3
x
y=3^{x}
y
=
3
x
\newline
(
2
2
2
)
y
=
log
x
3
y=\log _{x} 3
y
=
lo
g
x
3
\newline
(
4
4
4
)
x
=
3
′
′
x=3^{\prime \prime}
x
=
3
′′
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
z
2
y
\log \frac{x z^{2}}{y}
lo
g
y
x
z
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 x
lo
g
x
, and
log
y
\log y
lo
g
y
.
\newline
log
x
2
y
\log \frac{x^{2}}{y}
lo
g
y
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 x
lo
g
x
, and
log
y
\log y
lo
g
y
.
\newline
log
x
5
y
4
\log \frac{x^{5}}{y^{4}}
lo
g
y
4
x
5
\newline
Answer:
Get tutor help
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
2
\log \frac{x^{3}}{y^{2}}
lo
g
y
2
x
3
\newline
Answer:
Get tutor help
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
3
\log \frac{x^{5}}{y^{3}}
lo
g
y
3
x
5
\newline
Answer:
Get tutor help
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 \frac{x^{2}}{y^{4}}
lo
g
y
4
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
2
z
2
3
x
5
\log \frac{y^{2} \sqrt[3]{z^{2}}}{x^{5}}
lo
g
x
5
y
2
3
z
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
x
2
y
3
z
\log \frac{x^{2} \sqrt[3]{y}}{z}
lo
g
z
x
2
3
y
\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
z
4
y
4
3
\log \frac{x}{z^{4} \sqrt[3]{y^{4}}}
lo
g
z
4
3
y
4
x
\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
5
z
y
4
\log \frac{x^{5} z}{y^{4}}
lo
g
y
4
x
5
z
\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
5
y
2
z
3
\log \frac{x^{5}}{y^{2} z^{3}}
lo
g
y
2
z
3
x
5
\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
5
z
3
x
2
\log \frac{y^{5} \sqrt[3]{z}}{x^{2}}
lo
g
x
2
y
5
3
z
\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
z
4
y
3
x
\log \frac{z^{4} \sqrt[3]{y}}{x}
lo
g
x
z
4
3
y
\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
z
5
y
\log \frac{x}{z^{5} y}
lo
g
z
5
y
x
\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
z
5
x
\log \frac{y}{z^{5} x}
lo
g
z
5
x
y
\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
5
x
z
4
3
\log \frac{y^{5} x}{\sqrt[3]{z^{4}}}
lo
g
3
z
4
y
5
x
\newline
Answer:
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
2
log
b
9
2 \log _{b} 9
2
lo
g
b
9
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
log
b
10
+
log
b
8
\log _{b} 10+\log _{b} 8
lo
g
b
10
+
lo
g
b
8
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
4
log
b
2
+
log
b
5
4 \log _{b} 2+\log _{b} 5
4
lo
g
b
2
+
lo
g
b
5
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
log
b
3
+
log
b
2
\log _{b} 3+\log _{b} 2
lo
g
b
3
+
lo
g
b
2
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
2
log
b
3
2 \log _{b} 3
2
lo
g
b
3
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
3
log
b
4
3 \log _{b} 4
3
lo
g
b
4
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
log
b
9
−
log
b
9
\log _{b} 9-\log _{b} 9
lo
g
b
9
−
lo
g
b
9
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
2
log
b
3
+
log
b
6
2 \log _{b} 3+\log _{b} 6
2
lo
g
b
3
+
lo
g
b
6
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
log
b
4
−
log
b
4
\log _{b} 4-\log _{b} 4
lo
g
b
4
−
lo
g
b
4
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
log
b
7
+
log
b
9
\log _{b} 7+\log _{b} 9
lo
g
b
7
+
lo
g
b
9
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
3
log
b
3
3 \log _{b} 3
3
lo
g
b
3
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
log
b
5
+
log
b
4
\log _{b} 5+\log _{b} 4
lo
g
b
5
+
lo
g
b
4
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
4
log
b
2
4 \log _{b} 2
4
lo
g
b
2
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
2
log
b
5
2 \log _{b} 5
2
lo
g
b
5
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
2
log
b
8
2 \log _{b} 8
2
lo
g
b
8
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
5
log
b
2
−
log
b
4
5 \log _{b} 2-\log _{b} 4
5
lo
g
b
2
−
lo
g
b
4
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
2
log
b
4
2 \log _{b} 4
2
lo
g
b
4
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
log
b
2
+
2
log
b
2
\log _{b} 2+2 \log _{b} 2
lo
g
b
2
+
2
lo
g
b
2
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
log
b
6
+
log
b
7
\log _{b} 6+\log _{b} 7
lo
g
b
6
+
lo
g
b
7
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
log
b
10
−
log
b
10
\log _{b} 10-\log _{b} 10
lo
g
b
10
−
lo
g
b
10
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
5
log
b
2
5 \log _{b} 2
5
lo
g
b
2
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
log
b
6
−
log
b
2
\log _{b} 6-\log _{b} 2
lo
g
b
6
−
lo
g
b
2
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Write the expression below as a single logarithm in simplest form.
\newline
2
log
b
3
−
log
b
9
2 \log _{b} 3-\log _{b} 9
2
lo
g
b
3
−
lo
g
b
9
\newline
Answer:
log
b
(
□
)
\log _{b}(\square)
lo
g
b
(
□
)
Get tutor help
Condense the logarithm
\newline
5
log
b
+
3
log
r
5 \log b+3 \log r
5
lo
g
b
+
3
lo
g
r
\newline
Answer:
log
(
□
)
\log (\square)
lo
g
(
□
)
Get tutor help
Condense the logarithm
\newline
g
log
c
+
5
log
q
g \log c+5 \log q
g
lo
g
c
+
5
lo
g
q
\newline
Answer:
log
(
□
)
\log (\square)
lo
g
(
□
)
Get tutor help
1
2
Next