Why is the number of comparisons in a BST missing key lookup about 2 ln N?
The 2 comes from doing 2 comparisons at each node visited by the algorithm. The lg(n) comes from having to examine one node from each generation, or one node at each height in the tree. So, if we need to examine lg(n) nodes, and preform 2 operations at each node, we preform a total of 2lg(n) operations.