Logarithmic mean

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

for the positive numbers ${\displaystyle x,y}$. This calculation is applicable in engineering problems involving heat and mass transfer.

The logarithmic mean of two numbers is smaller than the arithmetic mean but larger than the geometric mean (unless the numbers are the same, in which case all three means are equal to the numbers):

From the mean value theorem

the logarithmic mean is obtained as the value of ${\displaystyle \xi }$ by substituting ${\displaystyle \ln }$ for ${\displaystyle f}$

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