My question is very fundamental clarification of maths regarding Log function. I do not understand why the example given on Wiki Fastai LogLoss page under Binary Classification has a Log function with negative domain (which afaik Log function would never take a negative number).

In the general formula given for binary classification the two probabilities are -> log( p ), log(1-p).
Yet in the example for mutli-class classification it is given value of log(0 - 0.25). Am I missing something?

Why function that takes value of form log( p ), log(1-p) is given log(0 - 0.25) = log(-0.25)?

The short answer is that the wiki is incorrect, and a log of a negative number is probably not what you want (it could yield an imaginary number, I suppose).