# Program to compute Log n

Write a one line C function that calculates and returns . For example, if n = 64, then your function should return 6, and if n = 129, then your function should return 7.

Using Recursion

## C

 `// C program to find log(n) using Recursion ` `#include ` ` `  `unsigned ``int` `Log2n(unsigned ``int` `n) ` `{ ` `    ``return` `(n > 1) ? 1 + Log2n(n / 2) : 0; ` `} ` ` `  `int` `main() ` `{ ` `    ``unsigned ``int` `n = 32; ` `    ``printf``(``"%u"``, Log2n(n)); ` `    ``getchar``(); ` `    ``return` `0; ` `}`

## Java

 `// Java program to find log(n) ` `// using Recursion ` `class` `Gfg1  ` `{ ` ` `  `    ``static` `int` `Log2n(``int` `n) ` `    ``{ ` `        ``return` `(n > ``1``) ? ``1` `+ Log2n(n / ``2``) : ``0``; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `n = ``32``; ` `        ``System.out.println(Log2n(n)); ` `    ``} ` `} ` ` `  `// This code is contributed by Niraj_Pandey `

## Python3

 `# Python 3 program to ` `# find log(n) using Recursion ` ` `  `def` `Log2n(n): ` ` `  `    ``return` `1` `+` `Log2n(n ``/` `2``) ``if` `(n > ``1``) ``else` `0` ` `  `# Driver code ` `n ``=` `32` `print``(Log2n(n)) ` ` `  `# This code is contributed by ` `# Smitha Dinesh Semwal `

## C#

 `// C# program to find log(n) ` `// using Recursion ` `using` `System; ` ` `  `class` `GFG { ` ` `  `    ``static` `int` `Log2n(``int` `n) ` `    ``{ ` `        ``return` `(n > 1) ? 1 +  ` `            ``Log2n(n / 2) : 0; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `n = 32; ` `         `  `        ``Console.Write(Log2n(n)); ` `    ``} ` `} ` ` `  `// This code is contributed by ` `// nitin mittal. `

Output :

```5
```

Time complexity: O(log n)
Auxiliary space: O(log n) if the stack size is considered during recursion otherwise O(1)

Using inbuilt log function

We can use the inbuilt function of standard library which is available in library.

## C

 `// C program to find log(n) using Inbuilt ` `// function of library ` `#include ` `#include ` `int` `main() ` `{ ` `    ``unsigned ``int` `n = 32; ` `    ``printf``(``"%d"``, (``int``)log2(n)); ` `    ``return` `0; ` `} `

## Java

 `// Java program to find log(n) using Inbuilt ` `// function of java.util.Math library ` `import` `java.util.*; ` ` `  `class` `Gfg2  ` `{ ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `n = ``32``; ` `        ``System.out.println((``int``)(Math.log(n) / Math.log(``2``))); ` `    ``} ` `} ` ` `  `// This code is contributed by Niraj_Pandey `

Output :

```5
```

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

# Let us try an extended version of the problem.

Write a one line function Logn(n, r) which returns .

Using Recursion

## C

 `// C program to find log(n) on arbitrary base using Recursion ` `#include ` ` `  `unsigned ``int` `Logn(unsigned ``int` `n, unsigned ``int` `r) ` `{ ` `    ``return` `(n > r - 1) ? 1 + Logn(n / r, r) : 0; ` `} ` ` `  `int` `main() ` `{ ` `    ``unsigned ``int` `n = 256; ` `    ``unsigned ``int` `r = 3; ` `    ``printf``(``"%u"``, Logn(n, r)); ` `    ``return` `0; ` `} `

## Java

 `// Java program to find log(n) on ` `// arbitrary base using Recursion ` `class` `Gfg3  ` `{ ` `    ``static` `int` `Logn(``int` `n, ``int` `r) ` `    ``{ ` `        ``return` `(n > r - ``1``) ? ``1` `+ Logn(n / r, r) : ``0``; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `n = ``256``; ` `        ``int` `r = ``3``; ` `        ``System.out.println(Logn(n, r)); ` `    ``} ` `} ` ` `  `// This code is contributed by Niraj_Pandey `

Output :

```5
```

Time complexity: O(log n)
Auxiliary space: O(log n) if the stack size is considered during recursion otherwise O(1)

Using inbuilt log function

We only need to use logarithm property to find the value of log(n) on arbitrary base r. i.e., where k can be any anything, which for standard log functions are either e or 10

## C

 `// C program to find log(n) on arbitrary base ` `// using log() function of maths library ` `#include ` `#include ` ` `  `unsigned ``int` `Logn(unsigned ``int` `n, unsigned ``int` `r) ` `{ ` `    ``return` `log``(n) / ``log``(r); ` `} ` ` `  `int` `main() ` `{ ` `    ``unsigned ``int` `n = 256; ` `    ``unsigned ``int` `r = 3; ` `    ``printf``(``"%u"``, Logn(n, r)); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find log(n) on arbitrary base ` `// using log() function of java.util.Math library ` `import` `java.util.*; ` ` `  `class` `Gfg4 { ` ` `  `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `n = ``256``; ` `        ``int` `r = ``3``; ` `        ``System.out.println((``int``)(Math.log(n) / Math.log(r))); ` `    ``} ` `} ` ` `  `// This code is contributed by Niraj_Pandey `

Output :

```5
```

Time complexity: O(1)
Auxiliary space: O(1)
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Improved By : Niraj_Pandey, nitin mittal

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