Why Logarithmic transformation?

I do classification for a living, and let's take Rahul's story as an example here. Rahul who is currently on my client's website, say Amazon.in, does he need some help in purchasing iPhone X that he is currently viewing? How do I classify whether he needs help or not? A simple googling shows that I need to do logistic regression. What's that?

Regression - To establish relationships with facts that I know, with the phenomenon that I am not aware of.

Logistic - I don't know, let's reason out now.

In order to estimate an unknown phenomenon of Rahul, all we can leverage is the known information about the subject. To understand whether Rahul will need help in purchasing iPhone X, we can leverage all the known information about Rahul. Which group does he belong to? Does he have Amazon prime membership? How often he visits PBN? and so on.

What do I need to estimate? whether he will need help in purchasing the phone or not. The answer needs to binary, however as nothing is certain, why not use probabilities? If the probability, p = 0 then the probability of Rahul needing help is 0 and when p=1 then it's 100% So, I need some kind of an equation that will give me a value that ranges between 0 and 1.

(Reference from CMU)

What makes odds ratio, that is, (p(x) / (1-p(x)) fit the bill in logistic transformation?

Simple, because odds ratio can vary between 0 and infinity, that is the exact constraint of x in log(x) = y. Mathematicians call it unbounded in one direction, that is it can increase in a positive direction, from 0 to infinity. If you are still curious, open up your calculator and try computing log (-1), it will throw an error.

(Reference from UCLA)

Now we kind of understand why we need logistic transformation for classification and odd's ratio is a bonus. Feel free to write back if you have something to talk about Logarithms, Classification, & Mathematics.

Vimal Kumar