This is a polynomial in [tex]2^x[/tex] that can be factorized:
[tex]2^{2x}-5\cdot2^x+4 = 0[/tex]
[tex]\left(2^x\right)^2-5\cdot2^x+4=0[/tex]
[tex]\left(2^x-4\right)\left(2^x-1\right)=0[/tex]
[tex]2^x-4=0\text{ or }2^x-1=0[/tex]
[tex]2^x=4\text{ or }2^x=1[/tex]
Since 4 = 2² and 1 = 2⁰, you get the two solutions x = 2 and x = 0.
