Log₂(x²-4)-3*log₂((x+2)/(x-2))≥2
log₂(((x-2)(x+2))-log₂((x+2)(x-2))³≥log₂4
ОДЗ: (x+2)(x-2)>0 x∈(-∞;-2)U(2;+∞)
log₂((x-2)(x+2)(x-2)³/(x+2)³))≥log₂4
log((x-2)⁴/(x+2)²)≥log₂4
(x-2)⁴/(x+2)²≥4
(x-2)⁴/(x+2)²-4≥0
((x-2)⁴-4*(x+2)²)/(x+2)²≥0
(x-2)⁴-(2*(x+2))²≥0
((x-2)²+2x+4)((x-2)²-2x-4)≥0
(x²-4x+4+2x+4)(x²-4x+4-2x-4)≥0
(x²-2x+8)(x²-6x)≥0
(x²-2x+1+7)*x*(x-6)≥0
((x-1)²+7)*x*(x-6)≥0
x*(x-6)≥0
-∞_______+_______0_______-________6_______+________+∞
x∈(-∞;0]U[6;+∞)
Учитывая ОДЗ:
x∈(-∞;-2)U[6;+∞).