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Cologarithmes.
Matériel didactique : La voie
Objectif opérationnel : Au terme de la leçon, l’élève sera capable de définir un cologarithme et de déterminer le cologarithme d’un nombre réel à l’aide des principes de base en 5 minutes.

Rappel

Calculez log 0,036749

Rappel

log⁡0,036749 = 2 ̅+log⁡3,6749

Motivation

Que donne log N ?

Donnez son expression mathématique ?

Motivation

Nombre                                              mantisse

1 →12\\ 0,9 →0,9.12 = 10,8\\ log⁡0,036749 = 56514+10,8\\ log⁡0,036749=2 ̅,5655248 = 56524,8

  • log N  donne cologarithme.
  • log N = colog.

 

 

Annonce du sujet

Qu'allons-nous étudier aujourd'hui ?

Annonce du sujet

Nous allons étudier aujourd'hui les cologarithmes.

Qu’appelle-t-on le cologarithme d’un nombre réel positif ?

Les cologarithmes

a. Définition : le cologaritme est le logarithme négatif d’un nombre réel. Ou encore ajouter l’opposé de logarithme.

b. Détermination de cologarithme

soit log N = c, m =(c+0, m)

colog N= - log N = - (c + 0, m) = -c-0, m

(on ajoute et on retranche 1)

            = - c -1+1-0,m = (-c-1) + (1-0,m)

                      Colog N  = -(c+1) + (1-0, m)

NB : - la caractéristique du cologarithme de N est –(c+1)

       - sa mantisse est la partie décimale de (1-0, m) soit 100.000 – m.

 

Exemple : 1. Log N = 4,89063

                    colog N = -4,89063 = *(4+1)+(1-0,89063) = -5+0,10937 = -5,10937.

2. log N = 7 ̅ =25682\\ Colog N = -7 ̅, 25682 = -(7 ̅+1)+(11-0,25682)\\ = -6 ̅ +0,74318\\ = - 6 ̅,74318

 

Qu’appelle-t-on le cologarithme d’un nombre réel nul ?

Est son logarithme négatif ou ajouter l’opposé de logarithme.

On donne log N, déterminez le colog N :

a. 2,56376\\ b. 7 ̅,09874\\ c. 1 ̅,00900\\ d. 0,89001

a. log 2,56376 = - 2,56376 = - (2+1)+(1-0,56376)\\ = -3+0,43624 = -3,43624\\ b. log 7 ̅,09874 = - 7 ̅,09874 = -(7+1) + (1-0,9874)\\ = -8+0,0126 = -8,0126\\ c. log 1 ̅,00900 = - 1 ̅, 09874 = - (1 ̅+1) + (1-0,09874)\\ d. log 0,89001 = -0,89001 = -(0+1) + (1-0,89001)\\ = - 1 + 0,1099 = - 1,1099.

Déterminez le colog N de :

a. 3 ̅,42979\\ b. 0,5289\\ c. 895,23

a. log 3 ̅,42979 = - 3 ̅, 42979 = - (3 ̅ + 9) + (1 – 0,42979) = - 2 ̅ + 0,57021 = -1,57021

MessagesTimelineExceptionsViews7RouteQueries44Models60GateSessionRequest
8.1.28PHP Version187msRequest Duration6MBMemory UsageGET lessons/{id}/{slug}Route
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