# Step-by-step Solution

## Expand the logarithmic expression $\log_{5}\left(x^85^2\right)$

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### Videos

$8\log_{5}\left(x\right)+2$

## Step-by-step Solution

Problem to solve:

$\log_{5}\left(5^2\right) x^8$

Choose the solving method

1

Calculate the power $5^2$

$\log_{5}\left(25x^8\right)$

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

$\log_{5}\left(25x^8\right)$

Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression log(5,5^2x^8). Calculate the power 5^2. Use the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right), where M=x^8 and N=25. Evaluating the logarithm of base 5 of 25. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x).

$8\log_{5}\left(x\right)+2$
SnapXam A2

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a
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m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
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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

$\log_{5}\left(5^2\right) x^8$

### Main topic:

Expanding Logarithms

~ 0.03 s