Wednesday, May 2, 2007

Prove If x>=4 THEN 2^x >= x^2

Currently, I'm working to prove If x>=4 THEN 2^x >= x^2

I can see that it is obviously true, but how to prove this. My first thought was to use induction.

I'll be thinking about this problem for today. It is from a book I am reading: Automata Theory, Languages, and Computation by Hopcroft, Motwani, and Ullman

2 comments:

NhatKiemXT said...

Currently, I'm working to prove If x>=4 THEN 2^x >= x^2

2^x for any x>0 the result will be even
x^2 for any x>0 the result will be even for every x even or odd for every x odd

therefore 2^x not equal x^2 when x >4 is odd number
...

Alex McFerron said...

I will try to prove this one too. Did you prove it already?