By | 24.03.2017

# 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 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 recursive call of the function.
• 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 : :

```/* 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 **************

************* 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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