sequences and series - How do I evaluate this sum :$sum_{n=1}^{infty}frac{{(-1)}^{n-1}log n}{n^s}$?

How do I evaluate this sum :

$$\sum_{n=1}^{\infty}\frac{{(-1)}^{n-1}\log n}{n^s}$$

Note : In wolfram alpha it is convergent for $Re(s)>1$ .!!

Thank you for any help