Log(x-1)^2 (x^2-4x+4)<0

Question

Log(x-1)^2 (x^2-4x+4)<0

Answer 1

ОДЗ
x-1≠0⇒x≠1
x-1≠1⇒x≠2
x-2≠0⇒x≠2
x∈(-∞;1) U (1;2) U (2;∞)
log(x-1)²(x-2)²<0<br>x∈(-∞;1)  U (2;∞)
(x-2)²<(x-1)²<br>(x-2)²-(x-1)²<0<br>(x-2-x+1)(x-2+x-1)<0<br>-(2x-3)<0<br>2x-3>0
2x>3
x>1,5
x∈(2;∞)
x∈(1;2)
x<1,5<br>x∈(1;1,5)
Ответ x∈(1;1,5) U (2;∞)