Question

$log _{x-3} ( x^{2} -12x+36) leq 0$

Answer 1

x-3>0⇒x>3
x-3≠1⇒x≠4
(x-6)²>0
x∈(3;4) U (4;6) U (6;∞)
1)x∈(3;4)
(x-6)²≥1
x²-12x+35≥0
x1+x2=12 U x1*x2=35⇒x1=5 U x2=7
x≤5 U x≥7
x∈(3;4)
2)x∈(4;6) U(6;∞)
(x-6)²≤1
5≤x≤7
x∈[5;6) U (6;7]
Ответ x∈(3;4) U [5;6) U (6;7]