# 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

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

## Javascript

 

Output:

3.000000

Time Complexity: O(1)

Auxiliary Space: O(1)

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