Why, why, why?
Why are you using a complicated natural logarithm?
A logarithmic ratio is used because that creates a sliding scale that recognizes the sliding scale of overhead inherent in hierarchical allocation of addresses. The natural logarithm was chosen because it is supported by both PERL and Excel.
The ratio works out the same no matter which logarithm is used. To see the sliding scale visually, check out the graphs on other slides in this presentation.