Q$6.(15$ points$)$

For each of the following pairs of functions, either $f(n)$ is in $O(g(n)),f(n)$ is in $(g(n)),$ or $f(n)=(g(n)),($i$.$e$.,f(n)$ is in both $O(g(n))$ and $(g(n)).$ Determine which relationship is correct, no explanation required.

$f(n)=lo{g}_2(2n)$;$g(n)=lo{g}_2(n)+2$

b$.f(n)=n^2+3n+4,g(n)=6n+7$

e$.f(n)=10$

d$.f(n)=logn+n$;$g(n)=nlogn$

e$.f(n)=2^n$;$g(n)=n^2$