Trying to find a closed form expression for the following sum, or an asymptotic expression in terms of well known functions (like the Gamma function, for instance).

Let $m,n$ be positive integers such that $2 \leq m < n$. Estimate the sum $$ \sum_{j=1}^m (-1)^j \binom m j \frac{\log(n-j)}{j} $$

where $\log$ stands for the natural logarithm. Thanks for any help.