Question

решить систему
9^x-3^(x+1)≥2*3^x-6
log8(x-0,5)(log8(8x-4)<0

Answer 1

3^2x-3*3^x-2*3^x+6>=0
3^x=t
t^2-5t+6>=0
t>=3
t<=2
3^x>=3  x>=1
3^x<=2  x<=lg3(2)
2x-1>0 x>1/2  (1/2;lg3(2)] U x>=1
lg8(2x-1)=t
(t-1/3)(t+2/3)<0
(t-1/3)(3t+2)<0
(-2/3;1/3)
1/4<2x-1<2
5/8<x<3/2
(1/2;lg3(2)] U x>=1

итого 1<=x<3/2U 5/8<x<=lg3(2)