# Correct order of the growth function [closed]

$5 \log( \log n)$

$n (\log n)^2$

$\sqrt{n} \log n$

$n^{\frac{4}{3}}$

$n \log (\log n)$

$7 \sqrt{n}$

What is the ascending order of the growth function? Please give the explanation as well.

## closed as off-topic by Antonio Vargas, gebruiker, Watson, Future, user228113 Jun 3 '16 at 16:32

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• What do you mean by correct order ? – Shailesh Jun 3 '16 at 6:32
• from most efficient to least efficient – Apples Jun 3 '16 at 6:39
• Do you have an idea of how any of them relate? – Henrik Jun 3 '16 at 15:18
• I know that logs are faster and fractional exponents are faster.But I don't have any depth of idea.Would you recommend something for a read? – Apples Jun 3 '16 at 16:17
• Well, out of the 30 possible pairs, some of are clearly asymptotically bigger than others. – user228113 Jun 3 '16 at 16:31

If you take sufficiently large value of n,then ascending order according to the value will be, $5 log( log n) < 7 \sqrt{n}<\sqrt{n} log n<n log (log n)<n (log n)^2<n^{\frac{4}{3}}$
$5 log( log n) > 7 \sqrt{n}>\sqrt{n} log n>n log (log n)>n (log n)^2>n^{\frac{4}{3}}$