Different home page for Visitors and Members?

This is the kind of fundamental question that reveals what a noob I really am.

I've got the home page of the Studio Theme starting to look like a sales page to entice visitors to register. But once they've registered and logged in, my members need a different kind of home page that shows all the social activity. But I'm not sure how to do that.

How can I redirect members to a different home from guests?

Thanks,
Lee