Lg(x-1)+lg(x-3)=lg(3/2 x-3)

Question

Lg(x-1)+lg(x-3)=lg(3/2 x-3)

Answer 1

ОДЗ
x-1>0⇒x>1
x-3>0⇒x>3
3/2x-3>0⇒3/2x>3⇒x>2
x∈(3;∞)
lg[(x-1)(x-3)]=lg(1,5x-3)
(x-1)(x-3)=1,5x-3
x²-3x-x+3-1,5x+3=0
x²-5,5x+6=0
D=30,25-24=6,25
x1=(5,5-2,5)/2=1,5не удов усл
x2=(5,5+2,5)/2=4