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(1/4)^x-(2)^x-1 -8<0

(1/4)^x-(1/2)^(x-1)-8<0
(1/2)^2x-2*(1/2)^x-8<0
(1/2)^x=v
v²-2*v-8<0   D=36
v₁=4   v₂=-2 
((1/2)^x-4)*((1/2)^x+2)<0
(1/2)^x+2 всeгда > 0 ⇒
(1/2)^x-4<0
(1/2)^x<4
(1/2)^x<(1/2)^(-2)
x>-2  ⇒
x∈(-2;+∞).