#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
long double B01LogFromE( long double x, long double k );
long double A02LogFromE( long double x, long double k );
long double A03LogFromE( long double x, long double k );

int main(int argc, char **argv)
{
   long double x;
   long double k = 2.;
   char pszString[256] = "2";

   if ( argc < 2 )
   {
      printf( "Enter a number to find logarithm base e of:" );
      fgets( pszString, sizeof( pszString ), stdin );
      puts( pszString );
   }
   else
      strncpy( pszString, argv[1], sizeof( pszString ) );

   k = atof( pszString );
   x = logl( k ); /* CORRECT ANSWER */

   printf("k           = %30.20LeL\nanswer      = %30.20LeL\n", k, logl( k ) );
   x = logl( k ) * 1.00001; /* form a extimate correct to 5 digits */

   printf( "B01LogFromE = %30.20LeL\n", B01LogFromE( x, k ) );
   printf( "A02LogFromE = %30.20LeL\n", A02LogFromE( x, k ) );
   printf( "A03LogFromE = %30.20LeL\n", A03LogFromE( x, k ) );

   return 0;
}

long double B01LogFromE( long double x, long double k )
{
   return ( k * x - expl( x ) + k ) / k;
}

long double A02LogFromE( long double x, long double k )
{
   long double ex = expl( x );
   return x + 2. * ( -ex + k ) / ( ex + k );
}

long double A03LogFromE( long double x, long double k )
{
   long double ex = expl( x );
   long double ex2 = ex * ex;
   long double k2 = k * k;
   long double term = 4.0 * ex * k + ex2 + k2;
   return ( x * term - 3.0 * ex2 + 3.0 * k2 ) / term;
}