Yes, I do. I write down very briefly the cases I did, at the end of each day, in the Notes app of my tablet/phone. It takes 30 seconds. It's not as detailed as my residency logs but, if asked, I can produce a list.
It looks like this: 3 gen surg ett 1 aline 1 cvc, 1 ortho spinal, 1 gyn mac, 1 gyn lma. You can be more specific than that, even use a spreadsheet. But the simpler it is, the higher the chances you will do it every day. In the end, what a credentialing committee wants to see is some kind of proof that you have provided the types of anesthesia and you have performed the types of procedures you are asking privileges for.
Some people collect the patients personal identification stickers in a notebook, with a short associated note. To me, that's a huge HIPAA risk.