Find the value of ln(N!) using Recursion

Given a number N, the task is to find the log value of the factorial of N i.e. log(N!).

Note: ln means log with base e.

Examples:

```Input: N = 2
Output: 0.693147

Input:  N = 3
Output: 1.791759
```

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

Approach:

Method -1: Calculate n! first, then take its log value.

Method -2: By using the property of log, i.e. take the sum of log values of n, n-1, n-2 …1.

ln(n!) = ln(n*n-1*n-2*…..*2*1) = ln(n)+ln(n-1)+……+ln(2)+ln(1)

Below is the implementation of the Method-2:

C++

 `// C++ implementation of the above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to calculate the value ` `double` `fact(``int` `n) ` `{ ` `    ``if` `(n == 1) ` `        ``return` `0; ` `    ``return` `fact(n - 1) + ``log``(n); ` `} ` `// Driver code ` `int` `main() ` `{ ` `    ``int` `N = 3; ` `    ``cout << fact(N) << ``"\n"``; ` `    ``return` `0; ` `} `

C

 `// C implementation of the above approach ` `#include ` `#include ` ` `  `long` `double` `fact(``int` `n) ` `{ ` `    ``if` `(n == 1) ` `        ``return` `0; ` `    ``return` `fact(n - 1) + ``log``(n); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 3; ` `    ``printf``(``"%Lf"``, fact(n)); ` `    ``return` `0; ` `} `

Java

 `// Java implementation of the above approach ` `import` `java.util.*; ` `import` `java.io.*; ` `class` `logfact { ` `    ``public` `static` `double` `fact(``int` `n) ` `    ``{ ` `        ``if` `(n == ``1``) ` `            ``return` `0``; ` `        ``return` `fact(n - ``1``) + Math.log(n); ` `    ``} ` ` `  `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` ` `  `        ``int` `N = ``3``; ` `        ``System.out.println(fact(N)); ` `    ``} ` `} `

Python

 `# Python implementation of the above approach ` `import` `math ` `def` `fact(n): ` `    ``if` `(n ``=``=` `1``): ` `        ``return` `0` `    ``else``:  ` `        ``return` `fact(n``-``1``) ``+` `math.log(n) ` `N ``=` `3` `print``(fact(N)) `

C#

 `// C# implementation of the above approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` `    ``public` `static` `double` `fact(``int` `n) ` `    ``{ ` `        ``if` `(n == 1) ` `            ``return` `0; ` `        ``return` `fact(n - 1) + Math.Log(n); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `N = 3; ` `        ``Console.WriteLine(fact(N)); ` `    ``} ` `} ` ` `  `// This code is contributed by ihritik `

PHP

 ` `

Output:

```1.791759
```

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Improved By : ihritik