$$log (x^{2}*y) + log \frac{1}{xy}=$$
you can't solve it because there is nothing on the other side of the equal sign.
However you can simplify it
$$\\log (x^{2}*y) + log \frac{1}{xy}\\=log (yx^{2}*\frac{1}{xy}) \\=log (x) \\$$