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Arithmetic-Logarithmic-Geometric Mean Inequality


\begin{displaymath}
{a+b\over 2} > {b-a\over\ln b-\ln a} > \sqrt{ab}.
\end{displaymath}

See also Napier's Inequality


References

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




© 1996-9 Eric W. Weisstein
1999-05-25