ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Expand the logarithmic expression $\log \left(10x^5\right)$

Go!
Symbolic mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

##  Final answer to the problem

$5\log \left(x\right)+1$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Solve for x
• Condense the logarithm
• Expand the logarithm
• Simplify
• Find the integral
• Find the derivative
• Write as single logarithm
• Integrate by partial fractions
• Product of Binomials with Common Term
Can't find a method? Tell us so we can add it.
1

Use the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$, where $M=x^5$ and $N=10$

$\log \left(x^5\right)+\log \left(10\right)$

Learn how to solve expanding logarithms problems step by step online.

$\log \left(x^5\right)+\log \left(10\right)$

Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression log(10*x^5). Use the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right), where M=x^5 and N=10. Evaluating the logarithm of base 10 of 10. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x).

##  Final answer to the problem

$5\log \left(x\right)+1$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Main Topic: Expanding Logarithms

Logarithm expansion consists of applying the properties of logarithms to express a single logarithm in multiple logarithms, usually much simpler.