How to prove $\log{n} = O(n^{0.5})$

Question

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

Answer 1

Hint:

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