Program to compute Log n

05 Oct, 2021
Write a one-line C function that calculates and returns . For example, if n = 64, then your function should return 6, and if n = 128, then your function should return 7.  
Using Recursion
C++
C
Java
Python3
C#
Javascript
// C++ program to find log(n) using Recursion#include <iostream>using namespace std; unsigned int Log2n(unsigned int n){    return (n > 1) ? 1 + Log2n(n / 2) : 0;} // Driver codeint main(){    unsigned int n = 32;    cout << Log2n(n);    getchar();    return 0;} // This code is contributed by kirti
// program to find log(n) using Recursion#include <stdio.h> unsigned int Log2n(unsigned int n){    return (n > 1) ? 1 + Log2n(n / 2) : 0;} int main(){    unsigned int n = 32;    printf("%u", Log2n(n));    getchar();    return 0;}
// Java program to find log(n)// using Recursionclass Gfg1{     static int Log2n(int n)    {        return (n > 1) ? 1 + Log2n(n / 2) : 0;    }         // Driver Code    public static void main(String args[])    {        int n = 32;        System.out.println(Log2n(n));    }} // This code is contributed by Niraj_Pandey
# Python 3 program to# find log(n) using Recursion def Log2n(n):     return 1 + Log2n(n / 2) if (n > 1) else 0 # Driver coden = 32print(Log2n(n)) # This code is contributed by# Smitha Dinesh Semwal
// C# program to find log(n)// using Recursionusing System; class GFG {     static int Log2n(int n)    {        return (n > 1) ? 1 +            Log2n(n / 2) : 0;    }         // Driver Code    public static void Main()    {        int n = 32;                 Console.Write(Log2n(n));    }} // This code is contributed by// nitin mittal.
<script>// program to find log(n) using Recursion     function  Log2n( n){    return (n > 1) ? 1 + Log2n(n / 2) : 0;}        n = 32;    document.write( Log2n(n));   //This code is contributed by simranarora5sos</script>
Output : 
5
Time complexity: O(log n) Auxiliary space: O(log n) if the stack size is considered during recursion otherwise O(1)  
Using inbuilt log function
We can use the inbuilt function of the standard library which is available in the library.  
C++
C
Java
Python3
C#
Javascript
// C++ program to find log(n) using Inbuilt#include <bits/stdc++.h>using namespace std; int main(){    unsigned int n = 32;    cout << (log(32) / log(2));    return 0;} // This code is contributed by UJJWAL BHARDWAJ
// C program to find log(n) using Inbuilt// function of <math.h> library#include <math.h>#include <stdio.h>int main(){    unsigned int n = 32;    printf("%d", (int)log2(n));    return 0;}
// Java program to find log(n) using Inbuilt// function of java.util.Math libraryimport java.util.*; class Gfg2{    public static void main(String args[])    {        int n = 32;        System.out.println((int)(Math.log(n) / Math.log(2)));    }} // This code is contributed by Niraj_Pandey
# Python3 program to find log(n) using Inbuilt # Function of math libraryimport math if __name__ == "__main__":    n = 32         print(int(math.log(n, 2)))     # This code is contributed by ukasp
// C# program to find log(n) using Inbuilt// functionusing System; class GFG{     static public void Main(){    int n = 32;    Console.WriteLine((int)(Math.Log(n) / Math.Log(2)));}} // This code is contributed by Ankita Saini
<script>//program to find log(n) using Inbuilt// function of <math.h> library      n = 32;     document.write(  Math.log2(n));//This code is contributed by simranarora5sos</script>
Output : 
5
Time complexity: O(1) Auxiliary space: O(1) 
Let us try an extended version of the problem.
Write a one line function Logn(n, r) which returns .  
Using Recursion 
C++
C
Java
Python3
C#
Javascript
// C++ program to find log(n) on arbitrary// base using Recursion#include <bits/stdc++.h>using namespace std; unsigned int Logn(unsigned int n,                  unsigned int r){    return (n > r - 1) ? 1 +       Logn(n / r, r) : 0;} // Driver codeint main(){    unsigned int n = 256;    unsigned int r = 3;         cout << Logn(n, r);         return 0;} // This code is contributed by UJJWAL BHARDWAJ
// C program to find log(n) on arbitrary base using Recursion#include <stdio.h> unsigned int Logn(unsigned int n, unsigned int r){    return (n > r - 1) ? 1 + Logn(n / r, r) : 0;} int main(){    unsigned int n = 256;    unsigned int r = 3;    printf("%u", Logn(n, r));    return 0;}
// Java program to find log(n) on// arbitrary base using Recursionclass Gfg3{    static int Logn(int n, int r)    {        return (n > r - 1) ? 1 + Logn(n / r, r) : 0;    }         // Driver Code    public static void main(String args[])    {        int n = 256;        int r = 3;        System.out.println(Logn(n, r));    }} // This code is contributed by Niraj_Pandey
# Python program to find log(n) on arbitrary# base using Recursiondef Logn(n, r):     return  1 + Logn(n / r, r) if (n > r - 1) else 0     # Driver coden = 256r = 3print(Logn(n, r)) # This code is contributed by shivanisinghss2110
// C# program to find log(n) on// arbitrary base using Recursionusing System; public class Gfg3{    static int Logn(int n, int r)    {        return (n > r - 1) ? 1 + Logn(n / r, r) : 0;    }         // Driver Code    public static void Main(String []args)    {        int n = 256;        int r = 3;        Console.WriteLine(Logn(n, r));    }} // This code is contributed by gauravrajput1
<script>//program to find log(n) on arbitrary base using Recursion       function Logn( n,  r){    return (n > r - 1) ? 1 + Logn(n / r, r) : 0;}        n = 256;     r = 3;    document.write( Logn(n, r));//This code is contributed by simranarora5sos</script>
Output : 
5
Time complexity: O(log n) Auxiliary space: O(log n) if the stack size is considered during recursion otherwise O(1) 
Using inbuilt log function
We only need to use the logarithm property to find the value of log(n) on arbitrary base r. i.e., where k can be any anything, which for standard log functions are either e or 10 
C++
C
Java
Python3
C#
Javascript
// C++ program to find log(n) on arbitrary base// using log() library function#include <bits/stdc++.h>using namespace std; unsigned int Logn(unsigned int n,                  unsigned int r){    return log(n) / log(r);} // Driver codeint main(){    unsigned int n = 256;    unsigned int r = 3;         cout << Logn(n, r);         return 0;} // This code is contributed by UJJWAL BHARDWAJ
// C program to find log(n) on arbitrary base// using log() function of maths library#include <math.h>#include <stdio.h> unsigned int Logn(unsigned int n, unsigned int r){    return log(n) / log(r);} int main(){    unsigned int n = 256;    unsigned int r = 3;    printf("%u", Logn(n, r));     return 0;}
// Java program to find log(n) on arbitrary base// using log() function of java.util.Math libraryimport java.util.*; class Gfg4 {     public static void main(String args[])    {        int n = 256;        int r = 3;        System.out.println((int)(Math.log(n) / Math.log(r)));    }} // This code is contributed by Niraj_Pandey
# Python program to find log(n) on arbitrary base# using log() library functionimport mathdef Logn(n, r):     return math.log(n) // math.log(r)  n = 256r = 3print(int(Logn(n, r)))     # This code is contributed by shivanisinghss2110
// C# program to find log(n) on arbitrary base// using log() function of java.util.Math libraryusing System; class Gfg4 {     public static void Main(String []args)    {        int n = 256;        int r = 3;        Console.Write((int)(Math.Log(n) / Math.Log(r)));    }} // This code is contributed by shivanisinghss2110
<script>// program to find log(n) on arbitrary base// using log() function of maths library    function  Logn( n, r){    return Math.floor(Math.log(n) / Math.log(r));}       n = 256;    r = 3;    document.write( Logn(n, r));//This code is contributed by simranarora5sos</script>
Output : 
5
Time complexity: O(1) Auxiliary space: O(1) 
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Niraj_Pandey
nitin mittal
simranarora5sos
ukasp
Kirti_Mangal
ankita_saini
its_codezada17
GauravRajput1
shivanisinghss2110
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CPP
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