The

logarithmic mean is a measure of central tendency for exponential series. There are two definitions of the logarithmic mean. The definitions are not equivalent, and selection of the proper logarithmic mean depends on the application.

The first definition of the logarithmic mean is used in many engineering problems involving heat and mass transfer (*e.g.* the design of heat exchangers). Most frequently it is used to express a log-mean temperature difference. The logarithmic mean of two values (X_{1}, X_{2}) is given by:

X_{lm} = (X_{2}- X_{1}) / ln(X_{2} /X_{1})

The second definition of the logarithmic mean is a more general one. This definition is also applicable to series of more than two elements:

X_{lm} = exp{{ln (X_{1}) + ln(X_{2}) + ... + ln(X_{N})} / N}