$($b$)$ Give an asymptotically tight bound $($i$.$e$.$ big$-)$ for the sum:

${\displaystyle \underset{i=1}{\overset{n}{}}}{i}^{r}lo{g}^s(i)$

where $r,s1$ and the notation $lo{g}^s(i)$ means raise $log(i)$ to the power of $s.$