Mathematical modelling with generalised logarithm and exponential functions

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 onit 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