$3\mathrm{.}1\mathrm{.}16$ Arrange the following functions into a list in which each function is little$-$oh

of the function that follows it$.$

$$n lg$($n$),$lg$($n$^10),$n$!,3,1/$lg$($n$),$ n$^(2)$lg$($n$),$n$^(5/2),2^(1+$lg$($n$),)[$lg$($n$)]^2,$lg$(10)^$n