The equation ${\log }_{3}x-{\log }_{x}3=2$ has 

$\begin{array}{r}{\log }_{3}x-{\log }_{x}3=2\\ \Rightarrow {\log }_{3}x-\frac{1}{{\log }_{3}x}=2\end{array}$
$\Rightarrow y-\frac{1}{y}=2,\text{ where }y={\log }_{3}x$
$y^2-2y-1=0$
is a quadratic equation in y with exactly two real roots.