Express the following functions in terms of the $\backslash$Theta $-$notation.

$($a$)2$n $+3$ log$100$ n$.$

$($b$)7$n$3+1000$n log n $+3$n$.$

$($c$)3$n$1\mathrm{.}5+($n$)$

$3$ log n$.$

$($d$)2$n $+100$n $+$ n$!.$