## Task A-3.1.

Determine all real numbers $a$ for which the equation

$$
|| 2^{x}-1|-2|=a
$$

has exactly two real solutions.
## First solution.

Let's solve the equation depending on the parameter $a$. First, note that for $a=2$ the equation has one solution: $x=\log _{2} 3$.

We conclude that the equation has exactly 2 solutions when $a \in\langle 0,1]$ and $a=2$.