black scholes - Intuition behind Ln transformation of stock price when applying Ito lemma

I am able to replicate steps and arrive to the option price using Black Scholes framework. Here however I am more interested to understand, at least intuitively, why the ln transformation of price process is performed (Ito lemma part) in the first place. Price process is already a function of time and Wiener process, so I wonder why do we need to apply another function (ln). I do not think it has to do with log normality of prices or normality of returns. I have seen such a transformation taking place in solution of other problems that were not related to GBM - BS framework.

Thanks,

Answer

This is merely a mathematical trick.

You cannot easily integrate $dS_t = S_t(\mu dt + \sigma dW_t)$ over time because the RHS depends on $S_t$.

Using Ito's lemma on the log price gets you: $d\ln(S_t) = \left(\mu-\frac{1}{2}\sigma^2\right) dt + \sigma dW_t$ which is straightforward to integrate.