Solve for $x$: ${\log }_2\left(x^2\right)-{\log }_2(x-1)=3$

$x=4-\sqrt{2}$

$x=4+\sqrt{2}$

$x=4-2\sqrt{2}$

$x=4+2\sqrt{2}$

$x=4-2\sqrt{2}$ only

$x=4+2\sqrt{2}$ only