Answer
$x=1000$
Work Step by Step
Using the properties of logarithms, the given expression, $
2\log x-\log x=3
,$ is equivalent to
\begin{array}{l}\require{cancel}
(2-1)\log x=3
\\\\
\log x=3
.\end{array}
Since $y=b^x$ is equivalent to $\log_b y=x$, then the solution to the equation, $
\log x=3
,$ is
\begin{array}{l}\require{cancel}
\log_{10} x=3
\\\\
x=10^3
\\\\
x=1000
.\end{array}
Upon checking, $
x=1000
$ satisfies the original equation.
