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## Homework Statement

Prove that [tex]2^{x} \geq x^{2}[/tex]

[tex]\forall x\geq5[/tex]

## Homework Equations

[tex]2^{k} \geq x^{k}[/tex]

## The Attempt at a Solution

I multiplied both sides by 2, then added to factor the RHS, and eventually got to the point where I just need to prove [tex]2^{n} \geq 2n+1[/tex] by induction also.