Question

$2^{2x-1}-7* 2^{x-1}+5 leq 0$

Answer 1

2²ˣ⁻¹-7*2ˣ⁻¹+5≤0
2²ˣ/2-7*2ˣ/2+5≤0   I×2
2²ˣ-7*2ˣ+10≤0
2ˣ=t  ⇒
t²-7t+10=0  D=9
t=5  2ˣ=5  log₂2ˣ=log₂5    x=log₂5≈2,32
t=2  2ˣ=2   x=1
(x-1)(x-2,32)≤0
-∞_______+_______1_______-_______2,32_________+_______+∞
x∈[1;log₂5].