how to bound above the following sequence

$\displaystyle f_{n}(x)=\Bigl(1-\frac{x}{n}\Bigr)^{n}\ln(x)$

since $\displaystyle \displaystyle\lim_{n\to\infty}\Bigl(1-\frac{x}{n}\Bigr)^{n}=e^{-x}$ we should probably bound above by the exponential function.

Someone knows how to do that?