Answer
$x=100$
Work Step by Step
Using the properties of logarithms, the given expression, $
3\log x-\log x^2=2
,$ is equivalent to
\begin{array}{l}\require{cancel}
3\log x-2\log x=2
\\\\
(3-2)\log x=2
\\\\
\log x=2
.\end{array}
Since $y=b^x$ is equivalent to $\log_b y=x$, then the solution to the equation, $
\log x=2
,$ is
\begin{array}{l}\require{cancel}
\log_{10} x=2
\\\\
x=10^2
\\\\
x=100
.\end{array}
Upon checking, $
x=100
$ satisfies the original equation.
