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Solve for n
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Solve for n (complex solution)
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625\times 25=5^{n-2}
Multiply both sides by 25, the reciprocal of \frac{1}{25}.
15625=5^{n-2}
Multiply 625 and 25 to get 15625.
5^{n-2}=15625
Swap sides so that all variable terms are on the left hand side.
\log(5^{n-2})=\log(15625)
Take the logarithm of both sides of the equation.
\left(n-2\right)\log(5)=\log(15625)
The logarithm of a number raised to a power is the power times the logarithm of the number.
n-2=\frac{\log(15625)}{\log(5)}
Divide both sides by \log(5).
n-2=\log_{5}\left(15625\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
n=6-\left(-2\right)
Add 2 to both sides of the equation.