Natural Logarithm of a Negative Number

Question

I am trying to find the genetic distance between two DNA sequences using Kimura (K80) model, and the formula contains natural logarithm, after calculating the required Q and P's needed, my solution looks like this: Click Here Since, natural logarithm of a negative number does not exist, how can I solve that equation?

Answer 1

maybe use that for $x<0$: $$ln(x) = i\pi + ln(|x|)$$