Remember, when talking about log odds with logistic regression, we always mean the natural logarithm of the odds (Ln[Odds]). Natural log is often abbreviated as “log” or “ln,” which can cause some confusion. In some contexts (not in logistic regression), “log” can be used as an abbreviation for base 10 logarithms. However, if used in the context of logistic regression, “log” means the natural logarithm!

Why is the natural log used instead of log base 10? Or log base 2? The short answer is tradition; that’s just the way it’s been done and so that’s how everyone does it.

However, there are some interesting properties of the natural logarithm (and its inverse - the exponential function) that have contributed to its use over potential alternatives. For example, take the exponential function:

exp(x) = ex

The derivative of this function is… itself! Additionally, the derivative of Ln(x) = 1/x. These properties - among some other convenient attributes when dealing with growth rates, interest rates, decay rates, etc. - have made the natural logarithm the log of choice.