Correct order of the growth function $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.
If you take sufficiently large value of n,then ascending order according to the value will be,
$5 log( log n)  &lt; 7 \sqrt{n}&lt;\sqrt{n} log n&lt;n log (log n)&lt;n (log n)^2&lt;n^{\frac{4}{3}}$

So,if we sort them from Most efficient to least efficient,it will be

$5 log( log n)  &gt; 7 \sqrt{n}&gt;\sqrt{n} log n&gt;n log (log n)&gt;n (log n)^2&gt;n^{\frac{4}{3}}$
If we want for sufficient large n, then if we name the equation from top to down as from 1 to 6 then ordering looks like 1&lt;5&lt;2 , 7&lt;3&lt;2 and 6&lt;4.