Solve for r
r=\frac{2}{3}\approx 0.666666667
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6^{3r}=36
Use the rules of exponents and logarithms to solve the equation.
\log(6^{3r})=\log(36)
Take the logarithm of both sides of the equation.
3r\log(6)=\log(36)
The logarithm of a number raised to a power is the power times the logarithm of the number.
3r=\frac{\log(36)}{\log(6)}
Divide both sides by \log(6).
3r=\log_{6}\left(36\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
r=\frac{2}{3}
Divide both sides by 3.
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