My math teacher had given me four problems on a sheet of paper, and I am unable to solve this last one:

Given that $x^{\log\_4(x - 2)} = 2^{3\log\_4(x-1)}$, solve for $x$.

I've tried numerous things such as simplifying the right hand side to $(x-1)^\frac{3}{2}$ and changing the left hand side to $(x-2)^{\log\_4x}$ to no avail.

From the way the question has been written, the equality could also be **read** as:
$x^{(\log\_4x)-2} = 2^{3(\log\_4x)-1}$

Edit:
It seems that the equation is supposed to be
$x^{(\log\_4x)-2} = 2^{3((\log\_4x)-1)}$

From WolframAlpha, I know the solutions are $x=2$ and $x=64$, but I don't know how to derive it.