Solve for m
m=8
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\frac{1}{125}\times 5^{m}=3125
Use the rules of exponents and logarithms to solve the equation.
5^{m}=390625
Multiply both sides by 125.
\log(5^{m})=\log(390625)
Take the logarithm of both sides of the equation.
m\log(5)=\log(390625)
The logarithm of a number raised to a power is the power times the logarithm of the number.
m=\frac{\log(390625)}{\log(5)}
Divide both sides by \log(5).
m=\log_{5}\left(390625\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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