In this episode we argue how and why we can devise an inverse function to the exponential function. Hence, we shall construct the logarithm and give precise reason why the logarithm exists and is indeed well-defined for any strictly positive real number. The existence part roots on the intermediate value theorem, the uniqueness part on the properties of the exponential function. The logarithm being the inverse of the exponential function is one of those functions that rather give the answer to a question (``To which power do I have to raise e to get a given number y?'') instead of being explicitly computable like the square or the reciprocal.