The product of the roots of the equation \(\log_{2} 2^{(\log_{2}x)^{2}} -5 \log_{2}x+6=0\) is

The product of the roots is 32. Setting $t=\log_2 x$ reduces the equation to $t^2-5t+6=(t-2)(t-3)=0$, so $x=4$ or $x=8$. Multiplying the logarithm values $2$ and $3$ before converting back to $x$ gives 6.