Number of digits in factorial

This program calculate how many digit in factorial of the number in given base
Anyone can just calculate number of digits in decimal, then b=10 always.

#include <stdio.h>
#include <math.h>
int main()
{
	int number,i,base,digit;
	double c,a=0;

	printf("Give the base and the number: ");
	scanf ("%d%d",&base,&number);

	c=log10(base);
	for (i=number;i>=1;i--) {

		a+=(log10(i))/c; 
	}
	digit=a+1;
	printf ("%d\n",digit);

	return 0;
}