I am sorry, but I have to disagree with you here. In my opinion the subscript button is better than a "logarithm with base b" button. It teaches the students to put the logarithm with base b together in much the same way that it would be done in many computer systems.
Also, this should not be added to the mqeditor.js code in the way that you are doing. That is certainly a massive hack. Just add it as a button in your problem in the same way that I added the subscript button. My method is not a hack. It is how I designed things to work, and is documented at https://webwork.maa.org/wiki/NamedAnswerRules.