It was part of my graph theory homework solution. The topic was about random graphs. I have difficulty understanding one step about log calculation. Hope someone could help me answer this: $\frac{\log(1-\frac{c\log n}{n})}{-\frac{c\log n}{n}}\cdot\frac{-c\log n}{n}(n-1)=\log n^{-(1+o(1))c}$. Here in this problem, the $o(1)$ notation is in terms of $n$.
Appreciate if you could answer it!