Solve the following equation:

$$
x^{2 \cdot \log _{2} x}=8
$$
Taking the base-2 logarithm of both sides of the equation, we get: $2\left(\log _{2} x\right)^{2}=3$. This equation has two solutions, $x_{1}=2^{\sqrt{3 / 2}} \approx 2.337$ and $x_{2}=2^{-\sqrt{3 / 2}} \approx 0.428$.