Can logarithm and polynomial transformation be included in the same equation Is it allowed to include logarithm and polynomial tranformations in the same econometric model.
For instance :
$$Y = x_1 + \log(x_2) + x_3 + x_3^2$$

I didn't find any interdiction however it seems to be not used in practise.

Thank you !
Yes it is "allowed". Econometrically it is not a problem. The real question is how useful such a model is for your setting and that will depend on your exact research question, variables and data.