Logarithmic mean

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In mathematics, the logarithmic mean is a function of two numbers which is equal to their difference divided by the logarithm of their quotient. In symbols:

[X_(a_1,a_2) = \frac}]

This measure is useful in engineering problems involving heat and mass transfer.

A different definition of logarithmic mean, applicable to more than two numbers, is the antilogarithm of the arithmetic mean of the logarithms:

[X_(a_1,a_2,a_3...a_n) = \exp( \frac \sum_^n \ln a_k)]

However, this definition is exactly equivalent to the geometric mean, so that term should be used instead of this one.

References

[Logarithmic mean@Everything2.com]
[Oilfield Glossary: Term 'logarithmic mean']

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