Question

$$\left. \begin{array} { l } { \log x = 6 \log y = - 2 } \\ { \quad \log ( x y ) } \end{array} \right.$$

Solve for x (complex solution)

$x=y^{6}$
$Im(\ln(y^{6}))-6Im(\ln(y))=0\text{ and }y\neq 0$

Solve for x

$x=y^{6}$
$y>0$