I'd rather ask a candidate to explain their favorite data structure to me and derive it's big-O complexity right then and there. Being able to regurgitate the correct answer doesn't count for anything in my book.
It is good to know what you should know about though.
... obviously they wanted 2, but O() doesn't work that way - changing base is a constant factor. Sometimes there's a tension between figuring out someone's understanding of the algorithm and someone's understanding of the notation (and math behind it). Of course, I gave them both answers...
Only if the base is constant. For example B-trees have O(log_B n)-time operations, and you can't ignore the B because it is a parameter (hence non-constant).