Write the code necessary to apply the following preprocessing steps $(3$ points$)$:

Define a recipe with name $$diamonds$\_$recipe$2.$

Make sure that price is your dependent variable and that you use all the other variables a predictors.

Log transform price and carat $($use base $2).$

Make sure infrequent values of all your nominal column are combined in an $$other$$ category.

Create a $$volume$$ column equal to x$*$y$*$z$.$

Keep only the rows with price bigger than $$3000$