Решите неравенство:
4^x-3 -71*2^x-6 +7 меньше или рано 0

4^(x-3) - 71*2^(x-6) + 7 ≤ 0
2^(2x-6) - 71*2^(x-6) + 7 ≤ 0
(1/64)*2^(2x) - (71/64)*2^(x) + 7 ≤ 0
Замена: 2^(x) = t > 0
(1/64)*t^2 - (71/64)*t + 7 ≤ 0
t^2 - 71t + 448 ≤ 0
D = 3249 = 57^2
t1 = (71-57)/2 = 7 > 0
t2 = (71+57)/2 = 64 > 0
7 ≤ t ≤ 64
7 ≤ 2^x ≤ 64
log2(7) ≤ x ≤ 6