Answer
$x=\frac{log(5)}{3log(6)}\approx.2994$
Work Step by Step
According to the logarithm property of equality $log_{b}a=log_{b}c$ is equivalent to $a=c$ (where a, b, and c are real numbers such that $log_{b}a$ and $log_{b}c$ are real numbers and $b\ne1$). We can use this property to solve for x.
$6^{3x}=5$
Take the common logarithm of both sides (which has base 10).
$log(6^{3x})=log(5)$
Use the power property of logarithms.
$3x log(6)=log(5)$
Divide both sides by $3log(6)$.
$x=\frac{log(5)}{3log(6)}\approx.2994$
