@ImFineAndYou? Filtering Log really doesn't drain your battery, the effect it has on battery juice and memory consumption is almost nonexistent. We plan to return the option to disable it, though, as a lot of users fell uneasy about it.
If you experience the battery drain with the latest AG beta, try looking into App Management to see if any app has an abnormally large amount of traffic consumed. There might be a loop that has to be fixed.