Решение
log₂ (x + y) + 2log₄ (x - y) = 5
3^(1 + 2*log₃(x - y) = 48
ОДЗ: x - y > 0
x + y > 0
log₂ (x + y) + log(₂²) (x - y)² = 5
3*[3^log₃ (x - y)²] = 48
log₂ [(x + y)*(x - y)] = 5
3*(x - y)² = 48
(x - y)² = 16
x - y = - 4 Не удовлетворяет ОДЗ
или x - y = 4
log₂[4*(x + y) = 5
4*(x + y) = 2⁵
4*(x + y) = 32
x + y = 8
x - y = 4
x + y = 8
складываем
2x = 12
x = 6
6 - y = 4
y = 2
Ответ: (6;2)