Jason Brimhall shows how to figure out who dropped that database:
What do you do when you run into that missing database situation and the inevitable denial that will ensue? This is when an audit can save the day. Through an audit, you can discover who dropped the database and when it happened. Then you have hard data to take back to the team to again ask what happened. Taking the info from a previous article of mine, we can alter the script I published there and re-use it for our needs here.
This is available in the default trace or, as Jason points out, you can create an Extended Event (which data can live much longer than that in the default trace).