Answer
$x=\dfrac{2}{3}$
Work Step by Step
Since $\log_b y=x$ implies $y=b^x$, the given equation, $
\log_3(6x+5)=2
$, implies
\begin{align*}\require{cancel}
6x+5&=3^2
\\
6x+5&=9
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
6x&=9-5
\\
6x&=4
\\\\
\dfrac{\cancel6x}{\cancel6}&=\dfrac{4}{6}
\\\\
x&=\dfrac{\cancelto24}{\cancelto36}
\\\\
x&=\dfrac{2}{3}
.\end{align*}
Hence, the solution to the equation $
\log_3(6x+5)=2
$ is $
x=\dfrac{2}{3}
$.
