Verified answer

2/(log(6)x +1) <= 1

ОДЗ x>0 log(6)x+1≠0 log(6)x≠-1 x≠1/6

x⊂(0 1/6) U (1/6 +∞)

2/(log(6)x +1) -1 <= 0

2/(log(6)x +1) -(log(6)x + 1)/(log(6)x +1) <= 0

(1- log(6)x)/(log(6)x +1) <= 0

log(6)x = t замена для простоты

(1-t)/(1+t) <=0

применяем метод интервалов

----------------- (-1) ++++++++ [1] ---------------

t<-1 t>=1

log(6)x<-1 x<1/6

log(6)x>=1 x>=6

объединяем с ОДЗ x⊂(0 1/6) U (1/6 +∞)

Ответ x⊂(0 1/6) U [6 +∞)