In the traditional text-book presentation and evaluation of logarithmic, exponential, circular and hyperbolic functions there is a lack of uniformity of method, and the demands on the analytical powers of the average student are considerable, if not excessive It has been shown in The Mathematical Gazette of June, 1926, that logarithmic and exponential functions may readily be evaluated by ab initio arithmetical methods. Incidentally it may be noted that the theory of the method is independent of the theory of indices. The definition of loge a is virtually and leads to a simple assignment of meaning to irrational and imaginary powers of a number.