Answer
$x=2$
Work Step by Step
Any solution x, if one exists, must be positive for the equation to be defined.
LHS: apply $\displaystyle \log_{a}\frac{M}{N}=\log_{a}M-\log_{a}N$
$\log_{10}10^{3}=3$, so we substitute this for the RHS.
$\log_{10} \displaystyle \frac{2000}{x} = \log_{10}1000$
... logarithmic functions are one-to-one, so
$\displaystyle \frac{2000}{x}=1000\qquad$ ... multiply with $\displaystyle \frac{x}{1000}$
$2=x$
