calculus - Show that if $1> x>0$, then $x-1 ≥ ln(x) ≥ 1−frac{1}{x}$

Show that if $0 < x < 1$, then

$$x-1 ≥ \ln(x) ≥ 1−\frac{1}{x}.$$

I know how to prove it using the MVT and I can prove it for $x> 1$ but I don't understand how to prove it for $x > 0$ .