There are plugins that do what you are wanting. Just search for custom logo and many will come up for you to choose from.
I am trying to do something similar, but also allowing login via facebook, twitter, etc. I was using Social Login for WordPress to allow facebook login. But then also used a plugin to change the login page by changing the logo and adding a photo, but social login then stopped working.
If you are not wanting login with facebook, it should be easy. If anyone has done both successfully, I would be interested in which two you used. I have very limited coding skill, so plugins are better for me.
yes, you find lot of plugins, like one Austin suggested, or you can customise on your own too, check wp docs:
http://codex.wordpress.org/Customizing_the_Login_Form
