# Nth root of a number using log

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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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, Apply logK on both the sides –
=> => => Below is the implementation of the above approach:

## C++

 // C++ implementation to find the  // Kth root of a number using log     #include     // 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

Output:

3.000000


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