The growth rate of the functions with respect to each other

Question

There are two functions , for example $f(n)=3\sqrt{n}$, and $g(n)=\log n$. Which one dominates, in other words, is $f(n)=O(g(n))$ or $f(n)= \Omega(g(n))$?

Thank you.

Answer 1

$f$ dominates. The logarithm function as $+\infty$ gets smaller than any power function.

Answer 2

$f$ can also be written as $f = 3\cdot n^{\frac{1}{2}}$, which is an exponential function in $n$, and hence it grows faster than $g$ (which is logarithmic).