Go to Settings>General>Usage>Battery Usage. Here you can see the list of apps that are using up your battery, for either the last 24 hours our the last 7 days.
When I checked mine for the last 24 hours, and the last 7 days, Facebook was right at the top. That tells me that I either need to keep that app closed, or maybe think about not using it on my phone. The kicker here is that Facebook is deeply embedded into the IOS operating system. It has bits running in the background, and you need to tweak a few other areas to make sure Facebook does not keep draining your battery.
To turn off Notifications for Facebook, go to Settings>Notifications. Find Facebook in the list and turn it off using the slider.
To turn off Location Services, go to Settings>Privacy>Location Services. Find Facebook in the list and change the setting from Always to Never, or When Using the App.
There you have it, the scoop on battery life. Go forth and conquer your technology!