Same problem here. Except mine won't even hold a charge now. My battery drained in less than 2 hours. I disabled maps, pulled the battery and sim, stopped running apps, and I just watched it have 18% battery and go down to zero in less than 1 minute. No joke. It seems that most of the battery drain is caused by the apps. I really don't know what to do at this point, but this is really upsetting. Nothing I've tried here has worked. What is this exchange account also? Any advice, help? Thanks!
Papa, the exchange account is one variety of "regular" email (not gmail), usually associated with a corporate email, or hotmail, or outlook. I suggest going to your email client (if you have one), removing your accounts, then go to settings -> apps -> all, delete data and cache for "exchange services". Reboot, then re-add your email account. For me it was an alternating combo of either exchange or maps devouring my battery life. I also suggest uninstalling maps, rebooting, then reinstalling (maybe delete data for maps as well for good measure before uninstalling).
For me I also did the following, based on another thread I found when digging around about the issue:
Cleared data and cache for the following processes: google account manager, google bookmarks sync, google contacts sync, google play services, google search, google services framework, and network location.
You might try these -if- fixing maps and/or exchange doesn't do it for you. My issues finally went away completely when I uninstalled maps and reinstalled, so it was either maps or (I suspect, based on what my "battery" settings were reporting) a number of things. I'm no expert, but these are the steps I took, and my phone is back to normal today. YMMV