I have the following inequality:
$$(1/2)log_2n >= 1$$
which I am trying to prove. More specifically, I am trying to find an integer N > 0 for which the inequality is true for all n >= N.
I know from substituting values, the inequality holds for all n >= 4.
However, I would like to prove the inequality in a better way. After all, you can't guarantee that the inequality holds for arbitrarily large values of n just from substituting values. What would be some techniques that I can use to prove that the inequality holds for all n >= N? Any insights are appreciated.
It is $$\frac{\ln(n)}{\ln(2)}\geq 2$$ so $$\ln(n) \geq 2\ln(2)$$ $$n\geq e^{2\ln(2)}=e^{\ln(4)}=4$$