Arrange the functions $n ^ { 3 / 2 } , \log \left( n ^ { n } \right) , \left( n ^ { 100 } \right) ^ { n }$ and $\log ( n ! )$ in a list so that each function is big-$O$ of the next function .

Question

Arrange the functions $n ^ { 3 / 2 } , \log \left( n ^ { n } \right) , \left( n ^ { 100 } \right) ^ { n }$ and $\log ( n ! )$ in a list so that each function is big-$O$ of the next  function .

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The Answer of Arrange the functions $n ^ { 3 / 2 } , \log \left( n ^ { n } \right) , \left( n ^ { 100 } \right) ^ { n }$ and $\log ( n ! )$ in a list so that each function is big-$O$ of the next  function .

Arrange the Functions n3/2,log⁡(nn),(n100)nn ^ { 3 / 2 } , \log \left( n ^ { n } \right) , \left( n ^ { 100 } \right) ^ { n }n3/2,log(nn),(n100)n

Arrange the Functions $n ^ { 3 / 2 } , \log \left( n ^ { n } \right) , \left( n ^ { 100 } \right) ^ { n }$