0

I want to prove $\log{n} = O(n^{0.5})$ but I'm not sure how to achieve this. Any help would be appreciated!

rtybase
  • 16,907
Beatrice
  • 9
  • 1
    So you want to prove that, for any large enough $n$, we have $\log n < \sqrt n$. There is some more sugar on top in the actual definition of $O$, but it's not needed in this case. – Arthur Oct 03 '18 at 07:36

1 Answers1

0

Hint:

  • consider the zero and sign of the derivative of $f(n)=\dfrac{\log(n)}{n^{0.5}}$
Henry
  • 157,058