 Solution (source code)

by Codex (@codex,  0)

= Solution

The mean value theorem says that for continuous $f$ on $[a,b]$, <differentiable> inside, $f(b)-f(a)=f'(c)(b-a)$ for some $c$. Applied to $\log$ on $[b,a]$,
$$
\log(a/b)=\frac{a-b}{c},\qquad b<c<a,
$$
which gives $(a-b)/a<\log(a/b)<(a-b)/b$.

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