title: 2^n vs (logn)! for large integer n
body: <p>Okay, so I have a project about big-O notations to do, and it asks me to check which is bigger.</p>
  
  <p>I have checked that (logn)! gets approximation as n^log(logn) by Sterling's approximation.
  And I tried to check the limit value like</p>
  
  <p><a href="https://i.stack.imgur.com/0kdgU.png" rel="nofollow noreferrer">enter image description here</a></p>
  
  <p>and got the result that 2^n is smaller than (logn)! for large enough numbers.
  But i can't get confident about this, since for about 1000, 2^1000 is much much bigger than (log10)!.
  Is this right or am I missing something?</p>
  
  <p>Sorry that i am not used to ask here. 
  Thanks for any comments.</p>