Arithmetic-Logarithmic-Geometric Mean Inequality

$${a+b\over 2} > {b-a\over\ln b-\ln a} > \sqrt{ab}.$$

See also Napier's Inequality

References

Nelson, R. B. ``Proof without Words: The Arithmetic-Logarithmic-Geometric Mean Inequality.'' Math. Mag. 68, 305, 1995.