TOPICS
Search

Arithmetic-Logarithmic-Geometric Mean Inequality

For positive numbers a and b with a!=b,

(a+b)/2>(b-a)/(lnb-lna)>sqrt(ab).

See also

Arithmetic Mean, Geometric Mean, Napier's Inequality

Explore with Wolfram|Alpha

References

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

Referenced on Wolfram|Alpha

Arithmetic-Logarithmic-Geometric Mean Inequality

Cite this as:

Weisstein, Eric W. "Arithmetic-Logarithmic-Geometric Mean Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Arithmetic-Logarithmic-GeometricMeanInequality.html

Subject classifications