I agree with Dude. We simply stopped doing the reading log, as it didn't make sense for us and was just a hassle. We occasionally mention the sorts of things DS has read recently, but we're not going to keep track of it. I doubt that the school in any district can condition a student's grades on the parent's performance of tracking activities anyway (i.e. parents can't be given homework).
There's certainly something to be said for not rocking the boat and being as pleasant as possible, but I think that the reading logs are a chance to remind the school/teacher that a child is far outside the norm, and a low-value way to get a teacher or admin to acknowledge that certain things are pointless for a child who's far ahead.
The only reason I'd do a reading log is to show the teacher how far ahead of the curve a student's reading really is, but in general I think that that's a weaker approach than relying on testing or other hard results, plus insistence on the ol' "evidence based practice". And DS brings a thick book to school often enough out of habit that his teacher has probably noticed. We haven't heard about the reading log in quite some time now.