Its a simple test. You log the predictor than create an interaction term between the original variable and the logged value. If this is significant in the regression model the original variables relationship is non-linear.

My problem is when ranking the effect size of variables, some of which are non-linear, I do not know how to evaluate the non-linear relationships relative importance. All the literature I know on non-linearity discusses evaluating it through graphs. Not how to evaluate the level of the parameter [I am not even sure you can interpret easily non-linear and linear parameters - but if there is a way to do so in terms of which is most important, I would love to know it].