f'(x)=e^x-k

(1) When k≤0, f(x) increases monotonically on R, and there is no minimum value for f(x).

(2) when k > 0, f(x) monotonically decreases at (-∞, lnk) and monotonically increases at [lnk,+∞), and f(x) has a minimum point x=ln k, and f(x) reaches a minimum value k -∞, lnk at x=lnk].

It can be seen from the above that k-lnk ≥ 0,0.