First of all, "working under the transform" means the opposite of what you write. It means working prior to the transform / on nodes before the transform.
If you want to work on a normalized image you will have to work on a node after the transform. If you want access to the log data, you will need to work on nodes before the transform. It can be more complex, but you are confused enough.
I suggest you watch the first lessons of this course, it explains the concept very well.