Please show steps and explain Put the following complexity c

Please show steps and explain. Put the following complexity classes in their proper order of containment. If any are equal, indicate that as well. 0(1.1^n), 0(n^3), 0(3^n), 0(ln(n)), 0(n!), 0(n^3 + n^2), 0(n100, ) 0 (n2^n), 0 (log10(n)), 0(10^100).

Solution

Given complexity classes:

0(1.1^n), 0(n^3), 0(3^n), 0(ln(n)), 0(n!), 0(n^3 + n^2), 0(n100, ) 0 (n2^n), 0 (log10(n)), 0(10^100).

       if we sustitue n=1

then,

   O(1.1),O(1),O(3),O(ln(1)),O(1),O(2),O(100),O(2),O(log10(1)),O(10^100)

From this,

      0(ln(n)),0 (log10(n)), 0(n!), 0(n^3), 0(1.1^n),0(n^3 + n^2), 0 (n2^n), 0(3^n), 0(n100),0(10^100).

in above wrote as proper order and equal are with bold.