Custom Admin Logo for WordPress 3.3.1 and newer

I found an article today with a bunch of tips for customizing WordPress, and tried to implement one to change the logo at the top left corner of the admin screen. There is normally a WordPress logo there. However, the code didn’t work. After poking around a bit, it became apparent that I must be using an out of date technique. After some further searching I found http://paulbredenberg.com/2012/01/changing-and-overriding-the-wordpress-admin-logo-since-3-3-1/

Here is what it looks like:

Thanks to Paul for providing updated code for the original solution found on wpbeginner.com.