Three hours if definitely NOT normal. I get at least 48 hours out my 2 year old iPhone 4S' battery with light usage. Did you do the iOS 7 update on the phone it self (OTA) or through iTunes? In my experience most problems are caused by the OTA updates. For this reason I ALWAYS update using iTunes on my computer.
I would suggest restoring your phone using iTunes on your computer and setting it us as a new phone. This downloads a fresh copy of iOS 7.1 from Apple and installs it on your phone. Just make sure that you transfer all purchased items (apps, music, etc.) as well as photos to your computer before restoring as the restore will completely wipe your phone. Do not restore from a back-up. Yes, you will loose all your data on the phone but restoring a back-up can restore the problem you are currently having back to your phone. Once your phone has been restored you can manually sync back your apps and music.
Before restoring you can also check to see that battery-killers like Location Services, Background App Refresh, etc are only turned on for the apps that really need it. I recently read and article that said that the Facebook app can be a real battery killer. If you have this app installed turn of location services and background app refresh for this app and see if that helps. Also go to Settings / General / Restrictions / Location Services / System Services and turn off all the options in that menu. Your phone does not need any of those to function. Constantly using your phone's GPS is a huge battery killer. I only have Location Services enabled for Find my iPhone and Background App Refresh is turned off completely.
I hope this helps.