Using log of function to determine orders of growth

Question

If I have functions $f(n)$ and $g(n)$ and I would like to determine $f(n) \in \Omega g(n)$ and/or $f(n) \in \Theta(g(n)$.

Does proving $\log(f(n)) \in \Omega \log(g(n))$ imply $f(n) \in \Omega g(n)$?

And similarly for $\Theta$?

Answer 1

Try $f(n)=n$ and $g(n)=n^c$ for various positive values of $c$, then check which of the properties $f\in\Theta(g)$, $f\in\Omega(g)$, $\log f\in\Theta(\log g)$ and $\log f\in\Omega(\log g)$, hold. Then write down the answer to your question here.