Dear experts, I am working with ecological data to fit regression model between green space accessibility (y) and some form of urban density (x2) on around 200 neighbourhoods with a certain % of specific age group (X1). The outcome variable is highly skewed (positive) so I have made log transform and it made the histogram look like normally distributed. However, bivariate scatter between Y and X2 is again showing a trend of non-linear relationship. Accordingly, a cubic function of X gives highest R-square value so is AIC/BIC value. So to make the model better can I use both log transformed outcome variable and polynomial function of X variable?

n.b. non-linear relation can be found even if the Y is not transformed but R-square is not as high as for transformed Y.