Step-by-step Solution

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

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Final Answer

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

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

Unlock this full step-by-step solution!

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).

Final Answer

$8\log_{5}\left(x\right)+2$
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a
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g
m
n
u
v
w
x
y
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.
(◻)
+
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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

Tips on how to improve your answer:

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

Main topic:

Expanding Logarithms

Related Formulas:

2. See formulas

Time to solve it:

~ 0.03 s