Answer
$x=\dfrac{17}{2}$
Work Step by Step
Since $\log_b y=x$ implies $y=b^x$, the given equation, $
\log_6(4x+2)=2
$, implies
\begin{align*}\require{cancel}
4x+2&=6^2
\\
4x+2&=36
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
4x&=36-2
\\
4x&=34
\\\\
\dfrac{\cancel{4}x}{\cancel{4}}&=\dfrac{34}{4}
\\\\
x&=\dfrac{\cancelto{17}{34}}{\cancelto24}
\\\\
x&=\dfrac{17}{2}
.\end{align*}
Hence, the solution to the equation $
\log_6(4x+2)=2
$ is $
x=\dfrac{17}{2}
$.
