If your logo is artistic enough (it has enough original material beyond text, even artistic treatment of text, to be considered "an original work of authorship"), you can copyright it with the US Copyright Office for $35. This would prevent anyone from using it without your express permission.
However, this probably isn't what you want -- you (or rather your friend) probably want to register it as a trademark, which is a different scope of protections. A trademark would protect the connection between the logo and the business (rather than just the picture itself), and it would prevent anyone from, for example, using the logo to designate their own business, thus confusing your customers.
The proper ownership of the logo is between you and your friend (do you really want to own your friend's business's trademark?). And I'm no legal advisor, but it seems to me that you should look into trademarks, not copyrights.
Hope this helps!