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Nth root of a number using log

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  • Last Updated : 18 Sep, 2022
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Given two integers N and K, the task is to find the Nth root of the K. 

Examples: 

Input: N = 3, K = 8 
Output: 2.00 
Explanation: 
Cube root of 8 is 2. i.e. 23 = 8

Input: N = 2, K = 16 
Output: 4.00 
Explanation: 
Square root of 16 is 4, i.e. 42 = 16 
 

Approach: The idea is to use logarithmic function to find the Nth root of K.

Let D be our Nth root of the K, 
Then, N^{\frac{1}{K}} = D
Apply logK on both the sides – 
=> log_{K}(N^{\frac{1}{K}}) = log_{K}(D)
=> \frac{1}{K} * log_{K}(N) = log_{K}(D)
=> D = K^{\frac{1}{K} * log_{K}(N)}
 

Below is the implementation of the above approach:  

C++




// C++ implementation to find the
// Kth root of a number using log
 
#include <bits/stdc++.h>
 
// Function to find the Kth root
// of the number using log function
double kthRoot(double n, int k)
{
    return pow(k,
               (1.0 / k)
                   * (log(n)
                      / log(k)));
}
 
// Driver Code
int main(void)
{
    double n = 81;
    int k = 4;
    printf("%lf ", kthRoot(n, k));
    return 0;
}

Java




// Java implementation to find the
// Kth root of a number using log
import java.util.*;
 
class GFG {
 
// Function to find the Kth root
// of the number using log function
static double kthRoot(double n, int k)
{
    return Math.pow(k, ((1.0 / k) *
                       (Math.log(n) /
                        Math.log(k))));
}
 
// Driver Code
public static void main(String args[])
{
    double n = 81;
    int k = 4;
     
    System.out.printf("%.6f", kthRoot(n, k));
}
}
 
// This code is contributed by rutvik_56

Python3




# Python3 implementation to find the
# Kth root of a number using log
 
import numpy as np
 
# Function to find the Kth root
# of the number using log function
def kthRoot(n, k):
     
    return pow(k, ((1.0 / k) *
                  (np.log(n) /
                   np.log(k))))
                    
# Driver Code
n = 81
k = 4
 
print("%.6f" % kthRoot(n, k))
 
# This code is contributed by PratikBasu   

C#




// C# implementation to find the
// Kth root of a number using log
using System;
 
class GFG {
 
// Function to find the Kth root
// of the number using log function
static double kthRoot(double n, int k)
{
     
    return Math.Pow(k, ((1.0 / k) *
                        (Math.Log(n) /
                         Math.Log(k))));
}
 
// Driver Code
public static void Main(String []args)
{
    double n = 81;
    int k = 4;
     
    Console.Write("{0:F6}", kthRoot(n, k));
}
}
 
// This code is contributed by AbhiThakur

Javascript




<script>
 
// Javascript implementation to find the
// Kth root of a number using log
 
// Function to find the Kth root
// of the number using log function
function kthRoot(n, k)
{
   return Math.pow(k, ((1.0 / k) *
                       (Math.log(n) /
                        Math.log(k))));
}
  
// Driver Code
var n = 81;
var k = 4;
var x = kthRoot(n, k)
 
document.write(x.toFixed(6));
 
// This code is contributed by Ankita saini
                     
</script>

Output: 

3.000000

 

Time Complexity: O(1)

Auxiliary Space: O(1)


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