upper bound of sequence of functions

upper bound of sequence of functions

What function will be an upper bound of the sequence
$f_{n}(x)=\Bigl(1-\frac{x}{n}\Bigr)^{n}\ln(x)$
since $\displaystyle\lim_{n\to\infty}\Bigl(1-\frac{x}{n}\Bigr)^{n}=e^{-x}$
so we should probably bound above by the exponential function.
Someone knows how to do that?