Mathc initiation/c81 d

Sommaire

Installer et compiler ces fichiers dans votre répertoire de travail.

	c0d.c

/* --------------------------------- */
/* save as c0d.c                     */
/* --------------------------------- */
#include "x_a.h"
#include  "fd.h"
/* --------------------------------- */
int main(void)
{
double x     = 3.;
double base  = 5.;

 clrscrn();
 
   printf(" The logarithm of x in base a is :  \n\n"
          "    log_a(x) = ln(x)/ln(a)        \n\n\n"
          " in C  you must write               \n\n"
          "    ln(x)/ln(a) as log(x)/log(a) \n\n\n\n");
          
          
   printf(" The logarithm of %.2f in base %.2f is : %f\n\n\n",
            x ,base, log_a(x, base));
            
/* with mathematica you can try log5(3) 
 * 
 *  log5(3) = 0.682606...               */

 stop();

 return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */

Vérifions par le calcul :

 The logarithm of x in base a is :  

    log_a(x) = ln(x)/ln(a)        


 in C  you must write               

    ln(x)/ln(a) as log(x)/log(a) 



 The logarithm of 3.00 in base 5.00 is : 0.682606


 Press return to continue.

Vérifions les égalités :

 Posons : 

 log_a(x)   = X             (1)


Introduisons a**() :

 log_a(x)      X 
a           = a

               X
       x    = a
 
 
 Introduisons ln() :
       
                    X
   ln(x)    =   ln(a)
   
   ln(x)    = X ln(a)
   
    ln(x)        
    -----   = X             (2) 
    ln(a)     
       
       
 Or nous avons (1) et (2)
       
   log_a(x) = X             (1)
   
 Donc 
    
     (1)        (2)
     
                ln(x)
   log_a(x)   = ----- 
                ln(a)