$5$ Comparing Algorithms $(15$ points$)$

For an array of size n $>1,$ suppose algorithm $($A$)$ takes $4$n $($logn$)2$ microseconds to process the

array and algorithm $($B$)$ takes $16$n$1/2$logn microseconds to do the same job:$1.$ For what values of n does program $($A$)$ take less time than $($B$)?$

$2.$ For each of these algorithms, what will be the time spent to process an array of size n $=2^10?$