Logging out from facebook on iphone?

When i log out from facebook on my iphone 5 it comes to the login screen, but it says "logged in as-myname-" continue? And under it says (not you) and if i press not you i can log into another account, but the problem is that when i wanted to use a different facebook account to sign into a website using my iphone it would only usd the facebook account that my phone said i was logged into, and not the one i just had logged onto. It may sound confusing but is there any way i could completely log out from facebook on my phone?

You can if you deactivate the app. Delete the app on your phone.

hope it helps.
Or go to your phone provider or even the Apple Store can help.

If I were you I would just go to the local phone provider place.