Question

log1/3(x^2+x-3) < -2

Answer 1

log₁/₃(x²+x-3)<-2
ОДЗ:  x²+x-3>0  D=13  x∈(-∞;≈-2.3)U(≈1,3;+∞)
log₁/₃(x²+x-3)<log₁/₃9
x²+x-3>9
x²+x-12>0  D=49
(x-3)(x+4)>0
-∞______+________-4________-_______3_______+______+∞
x∈(-∞;-4)U(3;+∞)  ⇒
Ответ: х∈(-∞;≈-2,3)U(3;+∞).