1. 4^ (2x) - 5*4^ (x) + 4<0

2. 7^ (x^2-2x-8/x+6) >=1

1) Замена 4^x = y

y^2 - 5y + 4 < 0

(y - 1) (y - 4) < 0

1 < y < 4

1 < 4^x < 4

4^0 < 4^x < 4^1

x ∈ (0; 1)

2) 7^[ (x^2-2x-8) / (x+6) ] > = 1

7^[ (x^2-2x-8) / (x+6) ] > = 7^0

(x^2-2x-8) / (x+6) > = 0

(x+2) (x-4) / (x+6) > = 0

x ∈ (-6; - 2] U [4; + oo)