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# Find Cube root of a number using Log function

• Last Updated : 17 Mar, 2021

Given number N, the task is to find the cube root using 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.
=> ∛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 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`

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