Solve for x
x=\frac{\log_{3}\left(85\right)}{5}\approx 0.808775089
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3^{5x}=85
Use the rules of exponents and logarithms to solve the equation.
\log(3^{5x})=\log(85)
Take the logarithm of both sides of the equation.
5x\log(3)=\log(85)
The logarithm of a number raised to a power is the power times the logarithm of the number.
5x=\frac{\log(85)}{\log(3)}
Divide both sides by \log(3).
5x=\log_{3}\left(85\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
x=\frac{\log_{3}\left(85\right)}{5}
Divide both sides by 5.
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