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:

$\begin{array}{ll} M_{\mbox{lm}}(x,y) &= \lim_{(\xi,\eta)\to(x,y)} \frac{\eta - \xi}{\ln \eta - \ln \xi} \\ &= \begin{cases} 0 & \mbox{if }x=0 \lor y=0 \\ x & \mbox{if }x=y \\ \frac{y - x}{\ln y - \ln x} & \mbox{else} \end{cases} \end{array}$

for the positive numbers . This calculation is applicable in engineering problems involving heat and mass transfer.

Read more about Logarithmic Mean: Inequalities, Connection To Other Means