Solve for n
n=1
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3^{4n}=81
Use the rules of exponents and logarithms to solve the equation.
\log(3^{4n})=\log(81)
Take the logarithm of both sides of the equation.
4n\log(3)=\log(81)
The logarithm of a number raised to a power is the power times the logarithm of the number.
4n=\frac{\log(81)}{\log(3)}
Divide both sides by \log(3).
4n=\log_{3}\left(81\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
n=\frac{4}{4}
Divide both sides by 4.
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