1) 2*2^(2x) - 5*2^x + 2 = 0
2^x =y, y > 0
2y^2 - 5y + 2 = 0
D= 25-4*2*2 = 9
y1 = (5-3)/4 = 1/2
y2 = (5+3)/8 = 2
2^x = 1/2
2^x = 2^(-1)
x1 = - 1
2^x = 2
x2 = 1
2) 3*(3^(2x) - 10*3^x + 3 = 0
3^x = y, y > 0
3y^2 - 10y + 3 = 0
D = 100 - 4*3*3 = 64
y1 = (10--8)/6 = 1/3
y2 = (10+8)/6 = 3
3^x = 1/3
3^x = 3^(-1)
x1 = -1
3^x = 3
x2 = 1
3) 4*(1/4)^(2x) + 15*(1/4)^x - 4 = 0
(1/4)^x = y, y > 0
4y^2 + 15y - 4 = 0
D 225 - 4*4*4 = 289
y1 (-15 - 17)/8 = -2
y2 = (-15 + 17)/8 = 1/4
(1/4)^x = - 2 не удовлетворяет условию: y> 0
(1/4)^x = 1/4
x = 1
4) (0,5)^(2x) + 1,5(0,5)^x - 1 = 0
(0,5)^x =y, y > 0
y^2 + 1,5x - 1= 0
D = 2,25 - 4*1*1 = 6,25
y1 = (-1,5 - 2,5) /2 = - 2
y2 = (-1,5 + 2,5)/2 = 1/2
(1/2^x = - 2 не удовлетворяет условию: y > 0
(1/2)^x = 1/2
x = 1