Can I change the color of the unity3d logo and place it on my blog web site?

Can I change the color of the unity3d logo and place it on my blog web site? For example: http://oriander.org/templates/oriander-template/images/oriander-mysql.png

No. Please don’t do that. Instead, if you want to let the world know your blog is about your use of Unity, please create your own logo which incorporates the Unity one. See http://www.unity3dstudent.com/ for an example of such a derived logo. The key thing is that it needs to be visibly not the Unity logo.