# Proving that a BST with N>=1 nodes will have log(N+1) levels

I am trying to prove by induction the following theorem: Use Induction to prove the following fact: for every integer, $N\ge 1$ , a BST with $N$ nodes must have at least $\log( N + 1)$ levels. I've proved the base case but I am struggling to figure out how to apply induction to prove for the $K+1$ case. Any suggestions would be wonderful.

• try to prove that any binary tree with $2^k$ nodes must have $k+1$ levels, it is better to avoid log. Jun 11 '13 at 16:21
• and remember that a binary tree= 1 root+ 2 binary trees Jun 11 '13 at 16:23
• Wonder if there is already a duplicate of this.
– Juho
Jun 11 '13 at 16:37
• Raphael's answer of Proving a binary tree has at most $\lceil n/2 \rceil$ leaves should help for this question as well. May 9 '14 at 10:36