2. Solve the equation

$$
2\left|\log _{1 / 2} x-1\right|-\left|\log _{4}\left(x^{2}\right)+2\right|=-\frac{1}{2} \log _{\sqrt{2}} x
$$
# Problem 2.

Answer: $\left(0 ; \frac{1}{4}\right] \cup\{1\}$ (variants V-1, V-2, V-4), $\left\{2^{-8 / 5} ; 1\right\}$ (variant V-3).

Solution (variant V-1). Rewrite the equation as

$$
\left|\log _{2} x+2\right|-2\left|\log _{2} x+1\right|=\log _{2} x
$$

and perform the substitution $t=\log _{2} x$. Solving the resulting equation $|t+2|-2|t+1|=t$ using the interval method, we get $t \in(-\infty ;-2] \cup\{0\}$.