Finally started to get some intuitive understanding of logarithms so I put it into code

logarithm.c

#include <stdio.h>
#include <stdlib.h>

int main(int argc, char *argv[]) {

    int base = atoi(argv[1]);
    int value = atoi(argv[2]);

    int i = 0;

    # keep dividing value by base to reverse the exponent processes
    while(value != 1) {

        # doesn't handle fractions
        if (value % base) {
            return -1;
        }

        # count how many divides it takes to reverse the process
        value = value / base;
        i++;
    }

    printf("%d\n", i);

    return 0;
}