Sol. If the numbers x and y satisfy this systems then they also satisfy the conditions

2–x > 0, 2 –x ≠ 1, 2x –2 > 0, 4 – y > 0,

4 – y ≠ 1, 2 – y > 0, i.e., the system of inequalities 1 < x < 2, y < 2 . On this domain for the bases of the logarithms of the initial system we have 0 < 2 – x < 1, 4 – y > 2

Thus the original system is equivalent to the system

⇒

Consequently, the set of all solutions of the original system is the set of pairs (x, y), where x- belongs to the interval (3/2, 2) and y belongs to the interval (1, 2).