Answer
$x=\dfrac{1}{3}$
Work Step by Step
Since $\log_b m=\log_b n $ implies $m=n$, then the given equation, $
\log (6x+1)=\log 3
$, implies
\begin{align*}\require{cancel}
6x+1&=3
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
6x&=3-1
\\
6x&=2
\\\\
\dfrac{\cancel6x}{\cancel6}&=\dfrac{2}{6}
\\\\
x&=\dfrac{\cancelto12}{\cancelto36}
\\\\
x&=\dfrac{1}{3}
.\end{align*}
Hence, the solution to the equation $
\log (6x+1)=\log 3
$ is $
x=\dfrac{1}{3}
$.
