FACEBOOK QUESTION. NEED HELP WITH.?

SOMEHOW AN APPLICATION WAS SENT FROM MY PROFILE BUT I DIDNT SEND IT. WHAT I WANT TO KNOW IS, IS THERE ANYWAY OF FINDING OUT EXACTLY WHAT TIME IT WAS SENT, HOW IT WAS SENT (MOBILE OR COMP) AND IF POSSIBLE WHAT IP ADDRESS IT WAS SENT FROM. THE ONLY PROBLEM WAS IT WAS SENT ON THE 28TH DECEMBER 2009. ALL YOUR HELP COULD BE VERY HELPFUL AS POLICE ARE INVOLVED IN THIS CASE. NO STUPID ANSWERS LIKE CHANGE YOUR PWORD. I NEED PROOF OF THESE FACTS AND QUICK. MANY THANKS.