"A 1-unit increase in log(x)log(x) is actually multiplying xx by ee (almost 3), which is a very different thing from adding 1 unit to xx. So the meaning of the estimated coefficient is totally different. You never need to transform your predictors to meet assumptions, as there are no assumptions on their distribution. Only outcomes have distributional assumptions in OLS. "

They argue that transforming a variable creates a totally new model as if you were adding or subtracting a variable.

Also it is commonly suggested to change predictors specifically to deal with the normality assumption. I know it is the residuals that matter here, which they don't really make clear, but the point is you are changing the predictor to deal with this. I have never heard it argued you should not do so because it creates a new model nor that you could not interpret it, assuming back transformations, in terms of the original model.

This one blew me away.