# Iterated Logarithm log*(n)

Iterated Logarithm or Log*(n) is the number of times the logarithm function must be iteratively applied before the result is less than or equal to 1. Applications: It is used in analysis of algorithms (Refer Wiki for details)

## C++

 // Recursive CPP program to find value of  // Iterated Logarithm  #include  using namespace std;     int _log(double x, double base)  {      return (int)(log(x) / log(base));  }     double recursiveLogStar(double n, double b)  {      if (n > 1.0)          return 1.0 + recursiveLogStar(_log(n, b), b);      else         return 0;  }     // Driver code  int main()  {      int n = 100, base = 5;      cout << "Log*(" << n << ") = "           << recursiveLogStar(n, base) << "\n";      return 0;  }

## Java

 // Recursive Java program to   // find value of Iterated Logarithm  import java.io.*;     class GFG  {  static int _log(double x,                   double base)  {      return (int)(Math.log(x) /                    Math.log(base));  }     static double recursiveLogStar(double n,                                  double b)  {      if (n > 1.0)          return 1.0 +                  recursiveLogStar(_log(n,                                    b), b);      else         return 0;  }     // Driver code  public static void main (String[] args)   {      int n = 100, base = 5;      System.out.println("Log*(" + n + ") = " +                    recursiveLogStar(n, base));  }  }     // This code is contributed by jit_t

## Python3

 # Recursive Python3 program to find value of  # Iterated Logarithm  import math     def _log(x, base):         return (int)(math.log(x) / math.log(base))     def recursiveLogStar(n, b):         if(n > 1.0):          return 1.0 + recursiveLogStar(_log(n, b), b)      else:          return 0       # Driver code  if __name__=='__main__':      n = 100     base = 5     print("Log*(", n, ") = ", recursiveLogStar(n, base))     # This code is contributed by  # Sanjit_Prasad

## C#

 // Recursive C# program to   // find value of Iterated Logarithm     using System;     public class GFG{  static int _log(double x, double baset)  {      return (int)(Math.Log(x) /                   Math.Log(baset));  }     static double recursiveLogStar(double n,                               double b)  {      if (n > 1.0)          return 1.0 +               recursiveLogStar(_log(n,                                   b), b);      else         return 0;  }     // Driver code      static public void Main (){             int n = 100, baset = 5;      Console.WriteLine("Log*(" + n + ") = " +                  recursiveLogStar(n, baset));  }  }     // This code is contributed by ajit.

## PHP

  1.0)          return 1.0 +                  recursiveLogStar(_log($n,   $b), $b);   else  return 0;  }    // Driver code  $n = 100; $base = 5;  echo "Log*(" , $n , ")"," = ",  recursiveLogStar($n, $base), "\n";     // This code is contributed by ajit  ?>

Output :

Log*(100) = 2


Iterative Implementation :

## C++

 // Iterative CPP function to find value of  // Iterated Logarithm  int iterativeLogStar(double n, double b)  {      int count = 0;      while (n >= 1) {          n = _log(n, b);          count++;      }      return count;  }

## Python3

 # Iterative Python function to find value of  # Iterated Logarithm        def iterativeLogStar(n, b):         count = 0     while(n >= 1):          n = _log(n, b)          count = count + 1        return count     # This code is contributed by  # Sanjit_Prasad

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