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

ОДЗ
x-1>0⇒x>1
5-x>0⇒x2x-3>0⇒x>1,5
x∈(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)2x²-12x+16=0
x²-6x+8=0
x1+x2=6 U x1*x2=8⇒x1=2 U x2=4
x-5=0⇒x=5
               _                +                      _                        +
-----------------(2)------------(4)------------------(5)---------------------
xx∈(1,5;2) U (4;5)