Solve for n
n=\frac{2}{3}\approx 0.666666667
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5^{3n}=25
Use the rules of exponents and logarithms to solve the equation.
\log(5^{3n})=\log(25)
Take the logarithm of both sides of the equation.
3n\log(5)=\log(25)
The logarithm of a number raised to a power is the power times the logarithm of the number.
3n=\frac{\log(25)}{\log(5)}
Divide both sides by \log(5).
3n=\log_{5}\left(25\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
n=\frac{2}{3}
Divide both sides by 3.
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