How to let Facebook Login button redirect to a particular URL - Facebook Stack Overflow

How to let Facebook Login button redirect to a particular URL - Facebook Stack Overflow: "
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This is the info on Facebook Login button

http://developers.facebook.com/docs/guides/web/

So it will render a Login button, and a user can click on it to log in on Facebook (a log in window will pop up) But after the user logs in, even though the Like or Share buttons work now, but the Log in button still shows.

1) Is there a way to redirect to a URL after the user successfully logs in?
2) Another way is to dynamically change the Log in button to invisible or better yet, show it as "Logged in as [Peter (username)]""

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