Algorithms Efficiency comparison function

Steps to compare functions 

•      Take log on both sides

•      Simplify function

•      Cancel values if any

•      Substitute values of n to see larger function

 Example

          2^n                                                                          n^2 

Take  Log on both sides

          L.H.S                                                       R.H.S

          Log 2^n                                                                 log n^2

          n log 2                                                                   2 log n

                n                                                                         2 log n

 
Put n = 2^100

            2^100                                                                    2 log 2^100

           2^100                                                                     2*100 log 2

         2^100                                                                     200 

So 2^n is larger