That wouldn't be a log (happenings in the order in which they happen), it would be a list, and someone would have to write an app to pull the data that way. If I could write Android apps (I don't know Android well enough to release anything I'd try writing), I'd dash off a little app to do it. It's a minor utility, maybe 25 lines of code. (I say maybe because I don't know how certain things have to be done in Android, but in, say, Windows, it would be a trivial app in any programming language.)