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  • 23-07-2021
  • Mathematics
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2^{2x}-5\cdot2^{x}+4=0

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LammettHash
LammettHash LammettHash
  • 23-07-2021

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.

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