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# Find Cube root of a number using Log function

• Last Updated : 14 Dec, 2022

Given the number N, the task is to find the cube root using the log function.
Examples:

Input: N = 8
Output: 2.000000
Input: N = 27
Output: 3.000000

Approach: To solve the problem mentioned above we will use log() function, according to the following formula:

Let cube root of N be d.
=> âˆ›N = d
=> N(1/3) = d
Now, apply log on both sides:
log3 (N(1/3)) = log3 (d)
=> log3 (d) = 1/3 * log3 (N)
=> d = 3(1/3 * log3 (N))

Below is the implementation of the above problem:

## C++

 // C++ program to Find Cube root // of a number using Logarithm   #include   // Function to find the cube root double cubeRoot(double n) {     // calculate the cube root     double ans = pow(3, (1.0 / 3)                             * (log(n) / log(3)));       // Return the final answer     return ans; }   // Driver code int main() {     double N = 8;       printf("%.2lf ", cubeRoot(N));       return 0; }

## Java

 // Java program to Find Cube root // of a number using Logarithm class GFG{       // Function to find the cube root static double cubeRoot(double n) {           // Calculate the cube root     double ans = Math.pow(3, ((1.0 / 3) *                               (Math.log(n) /                                Math.log(3))));       // Return the final answer     return ans; }   // Driver code public static void main(String[] args) {     double N = 8;     System.out.printf("%.2f", cubeRoot(N)); } }   // This code is contributed by Rajput-Ji

## Python3

 # Python3 program to find cube root # of a number using logarithm import numpy as np   # Function to find the cube root def cubeRoot(n):       # Calculate the cube root     ans = pow(3, (1.0 / 3) * (np.log(n) /                               np.log(3)))       # Return the final answer     return ans   # Driver code N = 8   print("%.2f" % cubeRoot(N))   # This code is contributed by PratikBasu

## C#

 // C# program to find cube root // of a number using logarithm using System;   class GFG{       // Function to find the cube root static double cubeRoot(double n) {           // Calculate the cube root     double ans = Math.Pow(3, ((1.0 / 3) *                               (Math.Log(n) /                                Math.Log(3))));       // Return the readonly answer     return ans; }   // Driver code public static void Main(String[] args) {     double N = 8;           Console.Write("{0:F2}", cubeRoot(N)); } }   // This code is contributed by sapnasingh4991

## Javascript



Output

2.00

Time complexity: O(log2(log3n))
Auxiliary space: O(1)

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