# 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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