Answer
$x=23$
Work Step by Step
Since $\log_b y=x$ implies $y=b^x$, the given equation, $
\log_5(5x+10)=3
$, implies
\begin{align*}\require{cancel}
5x+10&=5^3
\\
5x+10&=125
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
5x&=125-10
\\
5x&=115
\\\\
\dfrac{\cancel5x}{\cancel5}&=\dfrac{115}{5}
\\\\
x&=23
.\end{align*}
Hence, the solution to the equation $
\log_5(5x+10)=3
$ is $
x=23
$.
