2\(^{2x}\) -  5(2\(^x\)) + 4 = 0 

 2\(^{(x)2}\) - 5(2\(^x\)) + 4 = 0

let p = 2\(^x\)

 p\(^2\) - 5(p) + 4 = 0

p\(^2\) -4p - p + 4 = 0

p(p - 4) - 1(p - 4) = 0

(p - 1)(p -4) = 0

p = 1 or 4

But p = 2\(^x\) = 1 or 4

2\(^x\) = 2\(^2\)

x = 2

2\(^x\) = 2\(^0\) = 1

x = 0

Therefore, the values of x = 0 and 2