Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Precalculus
Properties of logarithms: mixed review
Expand the logarithm. Assume all expressions exist and are well-defined. 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.
log
v
7
\log v^7
lo
g
v
7
Get tutor help
Expand the logarithm. Assume all expressions exist and are well-defined. 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.
log
u
v
\log uv
lo
g
uv
Get tutor help
Add, subtract, multiply, or divide as indicated to simplify each expression. Remember to work within the parentheses first.
\newline
6
⋅
(
2
⋅
5
)
6\cdot(2\cdot5)
6
⋅
(
2
⋅
5
)
Get tutor help
Using distribution and combining the terms to simplify:
\newline
Simplify.
\newline
4
(
4
w
+
2
)
−
11
4(4w+2)-11
4
(
4
w
+
2
)
−
11
Get tutor help
Consider the equation
4
×
1
0
−
3
x
=
18
4\times 10^{-3x}=18
4
×
1
0
−
3
x
=
18
.
\newline
Solve the equation for
x
x
x
. Express the solution as a logarithm in base
−
10
-10
−
10
\newline
x
=
x=
x
=
□
\square
□
\newline
Approximate the value of
x
x
x
. Round your answer to the nearest thousandth.
\newline
x
≈
x\approx
x
≈
□
\square
□
Get tutor help
\newline
Write the log equation as an exponential equation.
\newline
log
5
x
(
x
+
1
)
=
8
3
\log _{5 x}(x+1)=\frac{8}{3}
lo
g
5
x
(
x
+
1
)
=
3
8
Get tutor help
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
Get tutor help
Write in exponential notation:
\newline
(
4
n
−
3
)
2
(4n^{-3})^{2}
(
4
n
−
3
)
2
Get tutor help
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
)
Get tutor help
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
≈
Get tutor help
log
(
10
×
x
−
3
)
\log(10 \times\sqrt{x-3})
lo
g
(
10
×
x
−
3
)
Get tutor help
