It's not just B-trees (and really, it would be simpler in a binary tree instead of a B-tree). In general, you can get those same asymptotic times with any balanced tree that stores at each node its number of children and their sum. The term for this kind of data structure is a monoid-cached tree, and it's a broadly useful pattern for doing fast incremental updates in a lot of different situations. Guy Steele has a few good examples in this talk (slides linked below the video):

http://vimeo.com/6624203