Answer
$\left\{\dfrac{11}{3}\right\}$
Work Step by Step
Since $\log_b x=\log_b y$ implies $x=y$, then the given equation, $
\log(3x-1)=\log10
$, implies
\begin{align*}
3x-1&=10
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
3x&=10+1
\\
3x&=11
\\\\
\dfrac{\cancel3x}{\cancel3}&=\dfrac{11}{3}
\\\\
x&=\dfrac{11}{3}
.\end{align*}
Hence, the solution set of the equation $
\log(3x-1)=\log10
$ is $
\left\{\dfrac{11}{3}\right\}
$.
