Answer
$x=4$
Work Step by Step
Since $\log_b y=x$ implies $y=b^x$, the given equation, $
\log_4(2x+8)=2
$, implies
\begin{align*}\require{cancel}
2x+8&=4^2
\\
2x+8&=16
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
2x&=16-8
\\
2x&=8
\\\\
\dfrac{\cancel2x}{\cancel2}&=\dfrac{8}{2}
\\\\
x&=4
.\end{align*}
Hence, the solution to the equation $
\log_4(2x+8)=2
$ is $
x=4
$.
