Question

2^{2x}-5\cdot2^{x}+4=0

Answer 1

This is a polynomial in
`2^x` that can be factorized:

`2^(2x)-5\cdot2^x+4 = 0`

`\left(2^x\right)^2-5\cdot2^x+4=0`

`\left(2^x-4\right)\left(2^x-1\right)=0`

`2^x-4=0\text{ or }2^x-1=0`

`2^x=4\text{ or }2^x=1`

Since 4 = 2² and 1 = 2⁰, you get the two solutions x = 2 and x = 0.