Show that if $1>x>0$, then $x-1\ge \mathrm{ln}(x)\ge 1-\frac{1}{x}$

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 $x>0$

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 $x>0$