1) 5^(x^2) - 15 = 25^x
5^(x^2) - 15 = 5^2x
x^2 - 15 = 2x
x^2 - 2x - 15 = 0
D = 4 + 60 = 64
X1 = (2+8)/2 = 5
X2 = (2-8)/2 = -3
Ответ: -3 ; 5.
2) 27^x < 9^(x^2) - 1
9^1,5 < 9^(x^2) - 1
1,5x < x^2 - 1
x^2 - 1,5x - 1 > 0
D = 2,25 + 4 = 6,25
X1 = (1,5+2,5)/2 = 2
X2 = (1,5-2,5)/2 = -0,5
Ответ: -0,5 ; 2.