Sure, if you are actually evaluating logarithm the base is very important. However, as I said, an entity designated as "O(log)" is exactly the same for every base so selecting a specific base here makes zero sense. Likewise, O(n^c) is as same as O() of any polynomial of power c, if somebody is writing O(3n^2 + 5n + 366) instead of O(n^2) - you know they don't quite understand what are they doing.
