Prove the following statement:

There is a real number x such that x>1 and $\displaystyle 2^x$ >x^(10)

I used a graphing calculator to find an X that works.. Determined that to be 59.. because 2^59 is giving me 5.8E17 vs x^10 which is giving me 5.1E17.. However, how do i solve this problem without the use of the calculator?