find function which is in o(log^k(n)) for fixed value of k and in ω(1)

Question

I need to find a function $f$ which is in $o(\log^{k} n)$ for fixed value of $k$ with $f = \omega(1)$. I know that for little $o$ the function should be strictly less than $c\log^k n$ for all $c$ and large enough $n$; and for little $\omega$ it should be strictly greater than $c\cdot 1$ for all $c$ and large enough $n$, but I am stuck here. How does one usually solve such type of problems?

Answer 1

Hint: Try $f(n) = \log\log n$.