Hand-coded log function won't find base-10 logs over 10

Question

As an assignment I'm coding a log function using the hi-lo method to find the answer, but what I have doesn't work for numbers greater than 10 and I can't figure out why

int main() {
  double n, nq, x, y;
  printf("Enter the number you wish to take to the base 10 logarithm:\n");
  scanf("%lf", &x);
  double hi = 1;
  double lo = 0;
  double qlo = 1;
  double qhi = 10;

  for(int i = 0; i <= 1000; i++) {
    n = ((lo + hi)/2);
    nq = sqrt(qlo * qhi);
    if(nq > x) {
      hi = n;
      qhi = nq;
    } else {
      lo = n;
      qlo = nq;
    }
  }
  y = n;

  printf("the logarithm is equal to %lf\n", y);
  printf("%lf\n", log10(x)); // to check result
}

Answer 1

Enter the number you wish to take to the base 10 logarithm:
1234.5678
50 iterations found 3.091514945509

See changes below...

#define  _CRT_SECURE_NO_WARNINGS

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

int main()
{
  double x, y;
  printf("Enter the number you wish to take to the base 10 logarithm:\n");
  scanf("%lf", &x);
  double hi = 1;
  double lo = 0;
  double qlo = 1;
  double qhi = 10;

  /*if (x <= 0) handle exception log undefined for input <= 0*/

  double tmp = 0;
  while (x > 10)
  {
    tmp++;
    x /= 10;
  }

  int i;
  double n = 0, nprev = -1;
  for (i = 0; i <= 1000 && fabs(n - nprev) > 1.0E-15; i++) 
  {
        nprev = n;
    n = ((lo + hi) / 2);
    double nq = sqrt(qlo * qhi);
    if (nq > x) 
    {
      hi = n;
      qhi = nq;
    }
    else 
    {
      lo = n;
      qlo = nq;
    }
  }
  y = tmp + n;
  printf("%2d iterations found %.12f",i,y);
}