is the kid to look at the log instead of the original thing when you're trying to maximize or minimize by taking the log at every point on the function you are doing monotonic transformations something was the highest point it'll still be the highest point for that function because the lowest still be the lowest the ordering stays the same so it's okay to take the log then the derivative becomes simple because we don't have this product of stuff anymore we have a sum of things because the log of the product is sum of the logs and we