1. Proving an Inequality

I was thinking of using convex function properties to prove the following inequality but couldn't. I'm not sure what else should I use.

$\displaystyle 1-(a/b)<ln(b/a)<(b/a) -1$
given that $\displaystyle 0<a<b$

2. Originally Posted by GIPC
$\displaystyle 1-(a/b)<ln(b/a)<(b/a) -1$
given that $\displaystyle 0<a<b$
Use the mean value theorem to prove Napier's inequality:
$\displaystyle \frac{1}{b}\le\frac{\log(b)-\log(a)}{b-a}\le\frac{1}{a}$.