I was curious about log and exp transformations. As far as I understood, we use them to transform non-linear relationship to linear. But doesn’t it kill the sole purpose of linear regression, if we are transforming the data to make it linear? in other words, if the relationship is not linear, why should we even transform the data and explore it with linear regression, instead of some other relationship or “algorithm”?

Additionally, there are different types of log transformations. Is there a guideline on which one to use, or is it a matter of preference of the user?