Question $17$

Consider the following three functions:

$f(n)=2^n**(logn{)}^{3}g(n)=n^2***2^{{?}^{?}}(logn)h(n)=n^{logn}{?}^{**}(logn)!$

Which of the following statements is TRUE about the asymptotic relationships between these functions?

$h(n)$ is $(f(n))$ and $g(n)$ is o$($f$($n$)),$ but $g(n)$ is not $(h(n))$

$g(n)$ is $(f(n))$ and $h(n)$ is $(g(n)),$ but $h(n)$ is not $O(f(n))$

$f(n)$ is o$($g$($n$))$ and $g(n)$ is $(h(n)),$ but $h(n)$ is not $(g(n))$

$f(n)$ is $O(g(n))$ and $g(n)$ is o$($h$($n$)),$ but $f(n)$ is not $(h(n))$