Recursive function

This program I wrote calculates the log of a certain number. Problem is we're supposed to use a recursive function, I tried to use one but the way I have it it could easily be replaced by putting the while loop around the whole function and not bothering at all with making it recursive. Any ideas on a better recursive function here? I'm new enough to programming, any help is much appreciated. Anyway here's the code

Code:

 #include <stdio.h>
#include <math.h>


float logarithm(float m, float n, float x, float y, float c);


int main(void)
{
	float m,n,x,y,c,ans;


	printf("******** WELCOME TO LOGGER ********");

	printf("\n\nEnter the lower value of range: ");
	scanf("%f", &m);
	
	printf("Enter the corresponding log (base 10): ");
	scanf("%f", &x);

	printf("\nEnter the highest value in range: ");
	scanf("%f", &n);

	printf("Enter the corresponding log (base 10): ");
	scanf("%f", &y);
	
	printf("\nEnter the value whose logarithm you wish to find: ");
	scanf("%f", &c);

	ans=logarithm(m, n, x, y, c);

	printf("\nThe estimated logarithm is %f", ans);
	

}


float logarithm(float m, float n, float x, float y, float c)

{
	float ans,g,a;

	

	g=sqrt(m*n);
	a=(x+y)/2;
	
	if (g<c)
	{
		m=g;
		x=a;
	}

	else if (g>c)
	
	{
		n=g;
		y=a;	

	}

	while ((fabs(m-n))>0.01)
	{
		return (logarithm(m, n, x, y, c));
	}

	return a;

}

By the way some guy called Napier came up with the algorithm, I know the maths is kind of confusing but it does work

Code:

float logarithm(float m, float n, float x, float y, float c)

{
	float ans,g,a;

	

	g=sqrt(m*n);
	a=(x+y)/2;
	
	if (g<c)
	{
		m=g;
		x=a;
	}

	else if (g>c)
	
	{
		n=g;
		y=a;	

	}

	while ((fabs(m-n))>0.01)
	{
		return (logarithm(m, n, x, y, c));
	}

	return a;

}

This is sort of recursive, but you're making it more complicated then it has to be, and thus losing much of the elegance of the recursive solution :

Code:

float logarithm(float m, float n, float x, float y, float c)

{
	float ans,g,a;

         /*  Add this part to eliminate the while loop */
	if((fabs(m-n))>0.01)
        {
                 return a;
        }

	g=sqrt(m*n);
	a=(x+y)/2;
	
	if (g<c)
	{
                /*   Don't do this
		m=g;
		x=a;
                */

                /*   Use this instead   */
                logarithm(g,n,a,y,c);
	}

	else if (g>c)
	
	{
                /*   Same as above 
		n=g;
		y=a;	
                */

                logarithm(m,g,x,a,c);
	}

        /*    Now this loop is useless
	while ((fabs(m-n))>0.01)
	{
		return (logarithm(m, n, x, y, c));
	}

	return a;
       */

}

Nice one, thanks for the help