Решите логарифмическое неравенство log9(x-1)-log9(5-x)>log9(2x-3)

ОДЗx-1>0⇒x>15-x>0⇒x<52x-3>0⇒x>1,5x∈(1,5;5)log(9)[(x-1)/(5-x)>log(9)(2x-3)(x-1)/(5-x)>2x-3(x-1)/(5-x) -(2x-3)>0(x-1-10x+15+2x²-3x)/(5-x)>0(2x²-12x+16)/(x-5)<02x²-12x+16=0x²-6x+8=0x1+x2=6 U x1*x2=8⇒x1=2 U x2=4x-5=0⇒x=5               _                +                      _                        +-----------------(2)------------(4)------------------(5)---------------------x<2 U 4<x<5 U x∈(1,5;5) x∈(1,5;2) U (4;5)