can you also show why? using their definitions so I can better understand it

Which of these is true, for functions:

f$($n$)=($log n$)^3$

g$($n$)=$ log $($n$^3)$

f$($n$)=$ o$($g$($n$))$

f$($n$)=\backslash$Theta $($g$($n$))$

f$($n$)=\backslash$omega $($g$($n$))$

None of these is true