Problem Detail: Is that statement false or true? I believe it’s false because ln(n) = log base e of n. So therefore, log base 2 of n can be a minimum because in 2^x = n, x will always be less than y in e^y = n. However can it ever be proven that log base 2 of n can be a maximum?
Asked By : Jonathan
Answered By : Luke Mathieson
Remember your log laws: $$ log_{a}b = frac{log_{x}b}{log_{x}a} $$ So $$ ln n = frac{log_{2}n}{log_{2}e} $$ Given this, can you think of three constants $c_{1}$, $c_{2}$ and $n_{0}$ such that $ln n leq c_{1}cdotlog_{2} n$ and $ln n geq c_{2}cdot log_{2}n$ for all $n geq n_{0}$?
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Question Source : http://cs.stackexchange.com/questions/48006
