Show that $\int_0^\infty \!\frac{e^{-x}-e^{-xt}}{x}\,\mathrm{d}x=\log(t)$

Question

I have tried a lot of different integration methods and I can't solve it.

$$\int_0^\infty\! \frac{e^{-x}-e^{-xt}}{x}\,\mathrm{d}x=\log(t)$$