Simply put, that rock hard, shudder-inducing turd that slides out of your dog’s anus that you KNOW you have to pick up. It’s that stiff turd that reveals how constipatedyour dog really is and how you should probably be feeding him name-brand kibble.
John: UR GRANNY TRANNY joe: I didn’t think it’d come to this..
John: wait-no-joe
Joe: ur dog log
John: soul leaves existence and everything is abolished
Dog it and log it is a phrase in similar vain to such phrases as "bag it and tag it" or "hump it and dump it". In this case, a guy gets a dirty dog out with a chick, typically of a drunken nature, and subsequently records the details of said dogging in a log of some kind.
Bill took a seat in front of the fireplace of his personal library. After putting his glasses on, he logged the dirty details of the previous night's debaucherous encounter.
Bro 1: Yo bro, did you get the dog out with that whore Stacy last night?
Bro 2:Yea bro, I dogged it and logged it.
Both: Dog 'N Log!