La definizione di funzione logaritmica \u00e8 la seguente: <\/p>\n
In matematica, le funzioni logaritmiche<\/strong> sono funzioni la cui variabile indipendente x<\/em> fa parte dell’argomento di un logaritmo. In altre parole, sono i seguenti:<\/p>\n<\/p>\n Oro<\/p>\n<\/p>\n \u00c8 necessariamente un numero reale positivo e diverso da 1.<\/p>\n<\/div>\n Ad esempio, la seguente funzione \u00e8 logaritmica:<\/p>\n<\/p>\n Prima di discutere le caratteristiche delle funzioni logaritmiche, rivediamo brevemente il concetto di logaritmo:<\/p>\n Di<\/p>\n \u00e8 l’elemento a cui deve essere elevato il numero<\/p>\n in modo che il risultato sia il numero<\/p>\n Ricordiamo anche che il logaritmo naturale (o logaritmo naturale) \u00e8 equivalente al logaritmo la cui base \u00e8 il numero esponenziale e:<\/p>\n<\/p>\n Al contrario, la base viene solitamente omessa quando \u00e8 10. Questi tipi di logaritmi sono chiamati logaritmi decimali o algoritmi comuni: <\/p>\n<\/p>\n Un logaritmo ammette solo numeri positivi, quindi il dominio di una funzione logaritmica sar\u00e0 costituito da tutti i numeri che soddisfano questa condizione.<\/p>\n<\/div>\n Ad esempio, calcoleremo il dominio della seguente funzione logaritmica:<\/p>\n \n<\/p>\n L’argomento di un logaritmo deve essere maggiore di 0, perch\u00e9 non esistono n\u00e9 logaritmi di numeri negativi n\u00e9 logaritmi di 0. Dobbiamo quindi guardare quando l’argomento della funzione \u00e8 maggiore di zero:<\/p>\n<\/p>\n Ora risolviamo la disuguaglianza: <\/p>\n<\/p>\n Quindi l’argomento del logaritmo sar\u00e0 maggiore di zero se<\/p>\n<\/p>\n \u00e8 maggiore di 2. Pertanto, il dominio della funzione \u00e8 costituito da tutti i numeri maggiori di 2 (non inclusi): <\/p>\n<\/p>\n Tuttavia, la funzione \u00e8 crescente se la base \u00e8 nell’intervallo tra zero e uno.<\/p>\n \\bm{\\cap}<\/p>\n \\bm{\\tazza}<\/p>\n Nous allons ensuite voir avec un exemple comment repr\u00e9senter graphiquement une fonction logarithmique.<\/p>\n ” title=”Rendered by QuickLaTeX.com” height=”217″ width=”1518″ style=”vertical-align: -5px;”><\/p>\n f(x)=\\log_2 (x-1)<\/p>\n \\log_2 (x-1)<\/p>\n x-1>0x>1<\/p>\n X<\/p>\n \\text{Dom } f = (1,+\\infty)<\/p>\n x= 1.5 \\ longrightarrow \\ f(1.5)=\\log_2 (1.5-1)=-1<\/p>\n x= 2 \\ longrightarrow \\ f(2)=\\log_2 (2-1)= 0<\/p>\n x= 3 \\ longrightarrow \\ f(3)=\\log_2 (3-1) = 1<\/p>\n x= 5 \\ longrightarrow \\ f(5)=\\log_2 (5-1) = 2<\/p>\n x= 9 \\ longrightarrow \\ f(9)=\\log_2 (9-1) = 3<\/p>\n \\begin{array}{c|c} x & f(x) \\\\ \\hline 1,5 & -1 \\\\ 2 & 0 \\\\ 3 & 1 \\\\ 5 & 2 \\\\ 9 & 3 \\end{array }<\/p>\n Nous vous recommandons d’utiliser une calculatrice pour trouver les points dans le tableau des valeurs, car ils ne sont pas faciles \u00e0 calculer \u00e0 la main. Cependant, dans certaines calculatrices, seuls les logarithmes en base 10 peuvent \u00eatre calcul\u00e9s, auquel cas n’oubliez pas que vous pouvez trouver le r\u00e9sultat de n’importe quel logarithme en appliquant le changement de propri\u00e9t\u00e9 de base des logarithmes :” title=”Rendered by QuickLaTeX.com” height=”19″ width=”3068″ style=”vertical-align: -5px;”><\/p>\n \\log_2 0.5 = \\cfrac{ \\log 0.5 }{ \\log 2} = -1<\/p>\n Et enfin, nous joignons les points et allongeons la fonction : <\/p>\n Notez que la fonction de droite continue de cro\u00eetre jusqu’\u00e0 l’infini. En revanche, la fonction de gauche diminue mais n’atteint jamais x=1. M\u00eame s’il s’en rapproche beaucoup, il ne le touche jamais. Cela signifie que la droite x=1 est une asymptote verticale de la fonction. <\/p>\n Calculez le domaine de la fonction logarithmique suivante : ” title=”Rendered by QuickLaTeX.com” height=”347″ width=”4961″ style=”vertical-align: -5px;”><\/p>\n f(x)= \\log_8 4x<\/p>\n Il n’existe ni le logarithme d’un nombre n\u00e9gatif ni le logarithme de 0. Il faut donc regarder quand l’argument du logarithme est sup\u00e9rieur \u00e0 0 : ” title=”Rendered by QuickLaTeX.com” height=”54″ width=”2128″ style=”vertical-align: -20px;”><\/p>\n 4x>0 x>\\cfrac{0}{4} x>0 \\mathbf{Dom } \\ \\bm{f = (0,+\\infty)}<\/p>\n Trouvez le domaine de la fonction logarithmique suivante : ” title=”Rendered by QuickLaTeX.com” height=”60″ width=”582″ style=”vertical-align: -4px;”><\/p>\n f(x)= \\log(4-x)<\/p>\n Il n’existe ni le logarithme d’un nombre n\u00e9gatif ni le logarithme de 0. Il faut donc regarder quand l’argument du logarithme est sup\u00e9rieur \u00e0 z\u00e9ro : ” title=”Rendered by QuickLaTeX.com” height=”54″ width=”2145″ style=”vertical-align: -20px;”><\/p>\n 4-x>0-x>-4x<\\cfrac{-4}{-1} = 4<\/p>\n x<4 \\mathbf{Dom } \\ \\bm{f = (-\\infty,4)}<\/p>\n Repr\u00e9sentez la fonction logarithmique suivante sur un graphique : ” title=”Rendered by QuickLaTeX.com” height=”60″ width=”582″ style=”vertical-align: -4px;”><\/p>\n f(x)= \\log_2x<\/p>\n Tout d’abord, il faut calculer le domaine de la fonction logarithmique : ” title=”Rendered by QuickLaTeX.com” height=”54″ width=”1771″ style=”vertical-align: -20px;”><\/p>\n x>0 \\text{Dom } f = (0,+\\infty)<\/p>\n x= 0.5 \\ \\longrightarrow \\ f(0.5)= \\log_2 0.5= -1 x= 1 \\ \\longrightarrow \\ f(1)= \\log_2 1= 0 x= 2 \\ \\longrightarrow \\ f( 2)= \\log_2 2 = 1 x= 4 \\ \\longrightarrow \\ f(4)= \\log_2 4= 2 x= 8 \\ \\longrightarrow \\ f(8)= \\log_2 8= 3<\/p>\n \\begin{array}{c|c} x & f(x) \\\\ \\hline 0.5 & -1 \\\\ 1 & 0 \\\\ 2 & 1 \\\\ 4 & 2 \\\\ 8 & 3 \\end{array }<\/p>\n Enfin, nous repr\u00e9sentons les points sur le graphique et dessinons la fonction : <\/p>\n Notez que la fonction de droite continue de cro\u00eetre jusqu’\u00e0 l’infini. Par contre, \u00e0 gauche la fonction diminue mais ne croise jamais x=0. C’est parce que la fonction a une asymptote verticale sur l’axe Y. <\/p>\n Repr\u00e9sentez graphiquement la fonction logarithmique suivante : ” title=”Rendered by QuickLaTeX.com” height=”173″ width=”3070″ style=”vertical-align: -5px;”><\/p>\n f(x)= \\log_2 (x+2)<\/p>\n La premi\u00e8re chose \u00e0 faire est de calculer le domaine de la fonction logarithmique : ” title=”Rendered by QuickLaTeX.com” height=”53″ width=”1825″ style=”vertical-align: -19px;”><\/p>\n x+2>0 x>-2 \\text{Dom } f = (-2,+\\infty)<\/p>\n x= -1.5 \\ \\longrightarrow \\ f(-1.5)= \\log_2 (-1.5+2)= -1 x= -1 \\ \\longrightarrow \\ f(-1)= \\log_2 (-1 +2)=0 x = 0 \\ \\longrightarrow \\ f(0)=\\log_2 (0+2)=1 x= 2 \\ \\longrightarrow \\ f(2)=\\log_2 (2+2)=2 x= 6 \\ \\longrightarrow \\ f( 6)=\\log_2 (6+2)=3<\/p>\n \\begin{array}{c|c} x & f(x) \\\\ \\hline -1.5 & -1 \\\\ -1 & 0 \\\\ 0 & 1 \\\\ 2 & 2 \\\\ 6 & 3 \\end {array }<\/p>\n Enfin, nous tra\u00e7ons les points sur le graphique et tra\u00e7ons la fonction : <\/p>\n Notez que la fonction de droite continue de cro\u00eetre jusqu’\u00e0 l’infini. Par contre, \u00e0 gauche la fonction diminue mais ne croise jamais x=-2. C’est parce qu’il a une asymptote verticale \u00e0 x=-2. <\/p>\n Faites la repr\u00e9sentation graphique de la fonction logarithmique suivante : ” title=”Rendered by QuickLaTeX.com” height=”195″ width=”3059″ style=”vertical-align: -5px;”><\/p>\n f(x)=\\log_3x<\/p>\n La premi\u00e8re chose \u00e0 faire est de calculer le domaine de la fonction logarithmique : ” title=”Rendered by QuickLaTeX.com” height=”53″ width=”1825″ style=”vertical-align: -19px;”><\/p>\n x>0 \\text{Dom } f = (0,+\\infty)<\/p>\n x= 1 \\ \\longrightarrow \\ f (1)= \\log_3 1= 0 x= 3 \\ \\longrightarrow \\ f(3)= \\log_3 3= 1 x= 9 \\ \\longrightarrow \\ f(9)= \\log_3 9= 2 \\displaystyle x= \\cfrac{1}{3} \\ \\longrightarrow \\ f\\left( \\frac{1}{3} \\right)= \\log_3 \\frac{1}{3}= -1 \\displaystyle x= \\cfrac{1}{9} \\ \\longrightarrow \\ f\\left( \\frac{1}{9} \\right)= \\log_3 \\frac{1}{9}= -2<\/p>\n \\begin{array}{c|c} x & f(x) \\\\ \\hline 1 & 0 \\\\ 3 & 1 \\\\ 9 & 2 \\\\ \\frac{1}{3} & -1 \\\\[1.1 es] \\frac{1}{9} & -2 \\end{array}<\/p>\n Et pour finir, nous repr\u00e9sentons les points sur le graphique et peignons la fonction : <\/p>\n Notez que la fonction de droite continue de cro\u00eetre jusqu’\u00e0 l’infini. Mais \u00e0 gauche la fonction d\u00e9cro\u00eet bien qu’elle ne croise jamais x=0. C’est parce que la fonction a une asymptote verticale sur l’axe des ordonn\u00e9es. <\/p>\n Repr\u00e9sentez graphiquement la fonction suivante avec un logarithme : ” title=”Rendered by QuickLaTeX.com” height=”195″ width=”3181″ style=”vertical-align: -5px;”><\/p>\n f(x)= \\log_2 (1-x)<\/p>\n Avant de repr\u00e9senter graphiquement la fonction, il faut calculer son domaine : ” title=”Rendered by QuickLaTeX.com” height=”53″ width=”1817″ style=”vertical-align: -19px;”><\/p>\n 1-x>0-x>-1x<\\cfrac{-1}{-1} = 1<\/p>\n x<1 \\text{Dom } f = (-\\infty,1)<\/p>\n x= 0,5 \\ \\longrightarrow \\ f(0,5)= \\log_2 (1-0,5)=-1 x= 0 \\ \\longrightarrow \\ f(0)= \\log_2 (1-0)= 0 x = -1 \\ \\longrightarrow \\ f(-1)=\\log_2 (1-(-1))=1 x= -3 \\ \\longrightarrow \\ f(-3)=\\log_2 (1-(-3))= 2 x= -7 \\ \\longrightarrow \\ f(-7)=\\log_2 (1-(-7))=3<\/p>\n \\begin{array}{c|c} x & f(x) \\\\ \\hline 0.5 & -1 \\\\ 0 & 0 \\\\ -1 & 1 \\\\ -3 & 2 \\\\ -7 & 3 \\ end{ vettore}<\/p>\n Et pour finir, nous repr\u00e9sentons les points sur le graphique et tra\u00e7ons la fonction : <\/p>\n Notez que la fonction de gauche continue de cro\u00eetre jusqu’\u00e0 l’infini. Par contre, \u00e0 droite la fonction diminue mais ne croise jamais x=1. Par cons\u00e9quent, il a une asymptote verticale sur la droite x=1. <\/p>\n \u00c0 titre r\u00e9capitulatif, vous trouverez ci-dessous les propri\u00e9t\u00e9s des logarithmes au cas o\u00f9 vous auriez besoin d’effectuer des op\u00e9rations avec des fonctions logarithmiques :<\/p>\n ” title=”Rendered by QuickLaTeX.com” height=”195″ width=”5919″ style=”vertical-align: -5px;”><\/p>\n \\log(A\\cdot B) = \\log A + \\log B<\/p>\n ” title=”Rendered by QuickLaTeX.com” height=”41″ width=”943″ style=”vertical-align: -5px;”><\/p>\n \\displaystyle \\log \\left(\\frac{A}{B} \\right) = \\log A \u2013 \\log B<\/p>\n ” title=”Rendered by QuickLaTeX.com” height=”41″ width=”892″ style=”vertical-align: -5px;”><\/p>\n \\displaystyle \\log A^n = n\\cdot \\log A<\/p>\n ” title=”Rendered by QuickLaTeX.com” height=”41″ width=”807″ style=”vertical-align: -5px;”><\/p>\n \\displaystyle \\log \\sqrt[n]{A} =\\cfrac{\\log A}{n} $<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":" In questa pagina scoprirai cosa sono le funzioni logaritmiche e anche come rappresentarle su un grafico. Inoltre vedrai tutte le sue caratteristiche, come calcolarne il dominio e diversi esempi per capirlo meglio. Infine, potrai esercitarti con esercizi e problemi risolti passo dopo passo sulle funzioni logaritmiche. Cos’\u00e8 una funzione logaritmica? La definizione di funzione logaritmica …<\/p>\n![\"f(x)=\\log_a](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-996f68a990550949a528d4b15cd61405_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"a\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" "\\"Rendered")
<\/p>\n![\"f(x)=\\log_5](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f5fa510df7de3c79482a4923a99fb6a0_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n\n
<\/p>\n![\"y\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"y.\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-62f853fa6f372493298c507883a9f490_l3.png\" "\\"Rendered")
<\/p>\n<\/li>\n<\/ul>\n![\"\\log_a](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a4cde96df4335f4e0b1e222ac1e066e2_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\ln](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1febea2ae7232e777d779d4d0d9e56c_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\log_{10}](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fc3f62bdc84fbd101c67c578a1a8446f_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> Dominio di una funzione logaritmica <\/span><\/h2>\n
![\"f(x)=\\log_3](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c74c93eb851d6a3cd260d3392b60ee6f_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"2x-4](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bc56ccadb5ea7561d024f53807c455e7_l3.png\")
0″ title=”Rendered by QuickLaTeX.com” height=”14″ width=”82″ style=”vertical-align: -2px;”><\/p>\n<\/p>\n![\"2x](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-485b0757461f520e4e2f1be32c41ce18_l3.png\")
4″ title=”Rendered by QuickLaTeX.com” height=”14″ width=”52″ style=”vertical-align: -2px;”><\/p>\n<\/p>\n![\"x](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f9babc81a8e078c9ad02c8275dc70188_l3.png\")
\\cfrac{4}{2}” title=”Rendered by QuickLaTeX.com” height=”38″ width=”45″ style=”vertical-align: -12px;”><\/p>\n<\/p>\n![\"x](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b0d114ca900168936b5c270433aff883_l3.png\")
2″ title=”Rendered by QuickLaTeX.com” height=”14″ width=”42″ style=”vertical-align: -2px;”><\/p>\n<\/p>\n![\"x\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" "\\"Rendered")
<\/p>\n![\"\\text{Dom](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b49703709c5c665a0facc9cf6809f2f_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> Caratteristiche delle funzioni logaritmiche<\/span><\/h2>\n
\n
\n
![\"\\text{Im](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a954b5c192478c3b7b14428ac8d5cbc_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n\n
\n
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1)” title=”Rendered by QuickLaTeX.com” height=”19″ width=”54″ style=”vertical-align: -5px;”><\/p>\n![\"(0](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a86971bd27ea9ede80ab8714850e2e6e_l3.png\")
\n<\/ul>\n\n
![\")](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25490d753a225086bfae4c0bd2e51229_l3.png\" "\\"Rendered")
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\n<\/ul>\n\n
<\/span> Comment repr\u00e9senter une fonction logarithmique sur un graphique<\/span><\/h2>\n
\n
![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ee812d965d2e5bb51ccc706c6bb48c14_l3.png\" "\\"Rendered")
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<\/p>\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-732f79bb88c25303dc4895f865c02279_l3.png\" "\\"Rendered")
<\/p>\n![\"est](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a112c9f4182790189c04241a71084ea_l3.png\" "\\"Rendered")
<\/p>\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b33056a86d70d2c199cf3419a9a922f_l3.png\")
\n\n
![\"<\/li](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1479456dcda042ce6ce4535b63e6a69e_l3.png\")
\n<\/ul>\n\n
\n<\/ul>\n\n
\n<\/ul>\n\n
\n<\/ul>\n\n
![\"<\/li](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f6cd5e35fb4aa49ccb62bf6ccadd7936_l3.png\")
\n<\/ul>\n<\/div>\n![\"<\/div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-668bd8c58422d58a80c4879d332573d7_l3.png\")
\n<\/div>\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-62a3e468e0d43f979309ccb2878eb961_l3.png\")
:<\/strong> <\/p>\n![""]("http:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/comment-representer-ou-graphiquer-une-fonction-logarithmique.webp")
<\/figure>\n<\/div>\n!["exemple]("http:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-representation-graphique-d-une-fonction-logarithmique.webp")
<\/figure>\n<\/div>\n<\/span> Exercices r\u00e9solus sur les fonctions logarithmiques<\/span><\/h2>\n
Exercice 1<\/h3>\n
![\"\n\n<div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-be7f21b839461337f07c2c015b7aa6c6_l3.png\")
\n![\"\n\n<div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7841aa49debde7e7151641bb088d7d23_l3.png\")
<\/div>\n Exercice 2<\/h3>\n
![\"\n\n<div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-90c3709a2ba0aea2d496aab2b1ccdbda_l3.png\")
\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-21981d3c89f1f8bea140b1a2e69e27b6_l3.png\" "\\"Rendered")
<\/p>\n![\"\n\n<div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-27387c74ff58d586c654fa99b7b318f4_l3.png\")
<\/div>\n Exercice 3<\/h3>\n
![\"\n\n<div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-307282d5c0871172708032bf0f6f2cbf_l3.png\")
\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a579608a1d544ae9cdbaadc110f51dfb_l3.png\")
x<\/em> dans l’intervalle du domaine : <\/p>\n![\"<\/div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2b3f5515ef8bc341d9a5520791d8a706_l3.png\")
\n![\"<\/div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c294f5ccb6844db8d2e3dcd7a6385795_l3.png\")
\n<\/div>\n!["exercices]("http:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/polynomes-p-icone.png")
<\/figure>\n<\/div>\n Exercice 4<\/h3>\n
![\"\n\n<div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fbf0b4b613094e7e5a8882805f0814e5_l3.png\")
\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a58be6aac2dee50ca7fe9cc22cdaeaa7_l3.png\")
x<\/em> dans l’intervalle de domaine : <\/p>\n\n![\"<\/div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9d14648fb900a7a600582fdf757b3339_l3.png\")
\n<\/div>\n!["exercice]("http:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/cropped-polynomials-p-icon.png.png"){kind=icon}
<\/figure>\n<\/div>\n Exercice 5<\/h3>\n
\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-70b63640315186b753ec3e9139853860_l3.png\")
\n\n![\"<\/div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4181c2e548adcb9703c6bf428b0c72d0_l3.png\")
\n<\/div>\n!["exemples]("http:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemples-de-fonctions-logarithmiques-ou-avec-logarithmes.webp")
<\/figure>\n<\/div>\n Exercice 6<\/h3>\n
![\"\n\n<div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5aee69b17d43fd128e22f5f41260988f_l3.png\")
\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b3b80efefee817b86a28526d78960ff_l3.png\" "\\"Rendered")
<\/p>\n![\"](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9b326f6c32bcb908d0eab60c1bcb0174_l3.png\")
x<\/em> dans l’intervalle de domaine : <\/p>\n\n![\"<\/div](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-826141d2d52e99c3486b8b379b2b2d46_l3.png\")
\n<\/div>\n!["fonction]("http:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/domaine-de-fonction-logarithmique.webp")
<\/figure>\n<\/div>\n<\/span>Propri\u00e9t\u00e9s des logarithmes<\/span><\/h2>\n
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![\"\n\n<ul](\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1a8646e21ba12be6d9fcc2c81dd7f3fc_l3.png\")
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\n