The usual method of developing the theory of the exponential and logarithmic functions is to take as a definition either

or

The first definition has the disadvantage that with it a good deal of the theory of series is needed. Neither development follows the lines on which the student first met the functions. A good deal could be said for the view that for most students the best type of accurate theory is one which fills up the gaps in methods which are already familiar The difficulties of taking

as a definition are well known.