Verified answer

Первое: (4/9)^x<=sqrt(2/3)

2x>=1/2

x>=1/4

Второе: замена t=log3(x), t!=0

(t-7)/(1/t-3)<=2

(7t-t^2)/(3t-1)<=2

(t^2-t-2)/(3t-1)>=0

(t-2)(t+1)/(3t-1)>=0

t in [-1, 0) U (0, 1/3)U[2,+infty)

x in [1/3, 1) U (1, 3^(1/3)) U [9, +infty)

Пересекаем с решением первого, в итоге имеем  [1/3, 1) U (1, 3^(1/3)) U [9, +infty)