Solve for n
n=3
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25\times 4^{n}=1600
Use the rules of exponents and logarithms to solve the equation.
4^{n}=64
Divide both sides by 25.
\log(4^{n})=\log(64)
Take the logarithm of both sides of the equation.
n\log(4)=\log(64)
The logarithm of a number raised to a power is the power times the logarithm of the number.
n=\frac{\log(64)}{\log(4)}
Divide both sides by \log(4).
n=\log_{4}\left(64\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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