Mathematical modelling with generalised logarithm and exponential functions

Baker, RD

Mathematical modelling with generalised logarithm and exponential functions

Baker, RD

Authors

RD Baker

Abstract

That `elementary transcendental function', the logarithm,
is a very familiar function, that we learn
early on, and I can still recall a mathematics teacher at school telling
the class solemnly that `all logarithms are indices'. It seemed like a
Zen koan at the time, but we were soon equipped with log tables and wrestling
with the mysteries of the `bar' notation. A lost art to the youth of today
who merely have to press the `ln' button on their calculator.

Quite a few years on
it seemed a good idea to try to generalise the logarithm and its inverse
function, the exponential, by adding a parameter. From a practical viewpoint,
this would mean that any model including logarithms or exponentials could
be immediately generalised in the attempt to fit data better.