4B. Find the set of solutions to the equation

$$
\log _{2}\left[1+\log _{2}\left(1+\log _{2} x\right)\right]=\sqrt{\frac{1}{2} x-x^{2}}
$$
Solution. It must be $1+\log _{2} x>0$, i.e., $x>\frac{1}{2}$. Also, it must be $\frac{1}{2} x-x^{2} \geq 0$ from which it follows that $0 \leq x \leq \frac{1}{2}$. Therefore, the set of solutions to the equation is the empty set.

## IV year