So I know that it is true for $n = 1$ because $h \ge \log(1)\implies h \ge 0$. I also assume that $n=k$ is true. But how would I prove $h \ge \log_2{k+1}$. I tried to through log laws, but I'm quite stuck.
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6Does this answer your question? Proving that a Binary Tree of $n$ nodes has a height of at least $\log(n)$. – poyea Mar 31 '21 at 05:31