Answer
$x=\dfrac{133}{12}$
Work Step by Step
Since $\log_b y=x$ implies $y=b^x$, the given equation, $
\log_5(12x-8)=3
$, implies
\begin{align*}\require{cancel}
12x-8&=5^3
\\
12x-8&=125
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
12x&=125+8
\\
12x&=133
\\\\
\dfrac{\cancel{12}x}{\cancel{12}}&=\dfrac{133}{12}
\\\\
x&=\dfrac{133}{12}
.\end{align*}
Hence, the solution to the equation $
\log_5(12x-8)=3
$ is $
x=\dfrac{133}{12}
$.
