Question

Помогите с показательным уравнением номер 26.Оно на фото.

Answer 1

8* (3^(x-2)/(3^x-2^x)) > 1 + (2/3)^x
8/9 * 3^x/(3^x-2^x) > 1+ (2/3)^x
8/9 * 1/(1-(2^x/3^x)) > 1+(2/3)^x
8/9 * 1/(1-(2/3)^x) > 1 + (2/3)^x
t=(2/3)^x

8/9 * 1/(1-t) > 1 + t
8/9(1-t)>1+t
8/9(1-t)-(1+t)>0
8-9(1-t^2)/9(1-t)>0
8-9+9t^2/(1-t)>0
9t^2-1/(1-t)>0
(t-1/3)(t+1/3)/(t-1)<0

   -             +                -           +
----(-1/3)------(1/3)-----(1)----->x

[t<-1/3
[1/3<t<1

[(2/3)^x<-1/3 (решений нет)
[1/3<(2/3)^x<1
0<x<log2/3(1/3)