# Find Cube root of a number using Log function

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

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

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 `

Output:

```2.00
```

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.