**C Program to calculate Base-2 and Base-N logarithm**

**C Program to calculate Base-2 and Base-N logarithm**

Write a C Program to calculate Base-2 and Base-N logarithm by recursion. Here’s simple Program to calculate Base-2 and Base-N logarithm using recursion in C Programming Language.

**Recursion : :**

**Recursion : :**

- Recursion is the process of repeating items in a self-similar way. In programming languages, if a program allows you to call a function inside the same function, then it is called a
of the function.**recursive call**

- The C programming language supports recursion, i.e., a function to call itself. But while using recursion, programmers need to be careful to define an exit condition from the function, otherwise it will go into an infinite loop.

- Recursive functions are very useful to solve many mathematical problems, such as calculating the factorial of a number, generating Fibonacci series, etc.

*Equation : :*

One can easily calculate the logarithm of any base using the following simple equation:

Where log *k* is the function that returns the base-k logarithm of a number, and it can be any real number.

Below is the source code for C Program to calculate Base-2 and Base-N logarithm by recursion which is successfully compiled and run on Windows System to produce desired output as shown below :

**SOURCE CODE : :**

**SOURCE CODE : :**

/* C Program to calculate Base-2 and Base-N logarithm by Recursion */ #include<stdio.h> int log2(int num); int logN(int num, int base); int main() { int num, base; printf("Enter number for Base-2 logarithm :: "); scanf("%d",&num); printf("\nValue of log base 2 of %d = %d\n",num,log2(num)); printf("\nEnter any number :"); scanf("%d",&num); printf("Enter base to %d :: ",num); scanf("%d",&base); printf("\nValue of log base %d of %d = %d\n",base,num,logN(num,base)); return 0; } int log2(int num) { if(num==1) return 0; return 1 + log2(num/2); } int logN(int num,int base) { if(num<base) return 0; return 1 + logN(num/base,base); }

**OUTPUT : :**

**OUTPUT : :**

************* OUTPUT ************** ************* FIRST RUN *********** Enter number for Base-2 logarithm :: 100 Value of log base 2 of 100 = 6 Enter any number :10 Enter base to 10 :: 10 Value of log base 10 of 10 = 1 ************* SECOND RUN *********** Enter number for Base-2 logarithm :: 2 Value of log base 2 of 2 = 1 Enter any number :100 Enter base to 100 :: 5 Value of log base 5 of 100 = 2

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