2*25^x-5*10^x+2*4^x=0

Question

2*25^x-5*10^x+2*4^x=0

Answer 1

Решение
2*5^(2x) - 5*(2^x)*(5^x) + 2*(2^2x) = 0    /( 2^2x)
2*(5/2)^(2x) - 5*(5/2)^x + 2 = 0
(5/2)^x = z
2*(z^2) - 5z + 2 =0
D = 25 - 4*2*2 = 9
z1 = (5 - 3) /4 = 1/2
z2 = (5 + 3)/4 = 2
(5/2)^x = 1/2
x = log(5/2)  1/2
(5/2)^x = 2
x = log(5/2)  2