1) 2^(x-1) = 2^(2/5) => x-1 = 2/5 x = 7/5
2) 2^(x+2) + 2*2^(x+1) = 4/2 => 2^(x+3) = 2^1 x+3 = 1 x = -2
3) 6^4x - 7* 6^2x + 6 = 0 6^((2x)^2) - 7 * 6^2x + 6 = 0
сделаем замену: 6^2x = t
t^2 - 7t + 6 = 0
D = 49 - 25
t1 = (7+5)/2 = 6 t2 = (7-5)/2 = 1
Обратная замена:
6^2x = 1 => x = 0
6^2x = 6 => x = 1/2
4)4^(x) - 4^(x-1) = 3 => 4*4^(x-1) - 4^(x-1) = 3
тогда 4^(x-1) = 4^0 x-1 = 0 => x = 1
5) 2^x + 5*2^(x+1) = 2^x + 10*2^x = 11/2
т.е. 2^x = 1/2 => x = -1