Решение
1/2log₂ (x-4)+1/2log₂ (2x-1)=log₂ 3
ОДЗ: x - 4 > 0, x > 4
2x - 1 > 0, x > 1/2
D(y) = (4; + ∞)
1/2log₂ (x-4)+1/2log₂ (2x-1)=log₂ 3 умножаем всё уравнение на 2
log₂ (x-4) + log₂ (2x-1 )= 2*log₂ 3
log₂ (x - 4)*(2x - 1) = log₂ 9
(x -4)*(2x - 1) = 9
2x² - x - 8x + 4 - 9 = 0
2x² - 9x - 5 = 0
D = 81 + 4*2*5 = 121
x₁ = (9 - √121)/4
x₁ = (9 - 11)/4
x₁ = - 1/2 ∉ (4; + ∞)
x₂ = (9 + √121)/4
x₂ = (9 + 11)/4
x₂ = 5 ∈ (4; + ∞)
Ответ: x = 5