If you go to Settings>Battery>Battery Usage, you'll be able to see what percentage of your battery usage was used by each app. This should enable you to see if the Facebook app is responsible for an inordinate percentage of your battery usage.Here's the the thing, if you've always had the facebook app on your phone you wouldn't really be able to tell if it's a big drain on your battery. The best way to decide is to delete the app and load facebook from your browser. You should be able to see pretty quickly
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