"log with the right base" doesn't make any difference. That's a linear mapping. For instance:

    2log x = log x / log 2 = ln x / ln 2

(With 2log the logarithm in base 2, log and ln the logarithm in bases you pick, but you can think of 10 and e)

See, for example, http://www.purplemath.com/modules/logrules5.htm, or derive it from the axioms.