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The logistic function is a function with domain and range the open interval, defined as: Equivalently, it can be written as: Yet another form that is sometimes used, because it makes some aspects of the symmetry more evident, is: For this page, we will denote the function by the letter.We may extend the logistic function to a function, where and.et another form that is sometimes used, because it makes some aspects of the symmetry more evident, is: For this page, we will denote the function by the letter. We may extend the logistic function to a function, where and.
The General Logarithmic Functions. The natural logarithm function is defined as the inverse of the natural exponential function. So it's perfectly natural to define the general logarithmic function as the inverse of the general exponential function. Consider y = 2, the exponential function of base 2, as graphed in Fig. 5.1. Clearly it's one-to-one, and so has an inverse. This inverse is called the logarithmic function of base 2 or logarithm of base 2, and denoted log 2. Thus if y = 2 then x = log 2 y.