Ẓṛ asagm n Alugaritm agaman

{{Amgrad icqqan}}[[Afaylu:Logarithme neperien.svg|thumb|325x325px|Alugaritm anipiri ]]Iga '''Alugaritm agaman''' nɣ '''Alugaritm anipiri''' (s [[tanglizt]] : Natural logarithm) yat tsɣnt bahra ittyusann ɣ [[tusnakt]]. Ar tsnfal tasɣnt ad afaris s tmrnit zun d [[Tasɣnt talugaritm|tisɣnin ilugaritmiyn]] yaḍnin. Ar tt nttara s mk ad : <math>\ln()</math>. 

Ar nttini is iga alugaritm agaman s uzadur n <math>e</math> acku <math>ln(e)=1</math>. Iga alugaritm agaman tamnzut n tsɣnt : <math>x \longmapsto 1/x </math> ɣ uzilal  <math>]0 ; + \infty[</math> .

== Amzruy ==
Alugaritm ad dars yan yism yaḍn ad t igan d "anipiri". Ism ad ikka d [[John Napir]], yan umusnak askatlandi, amskar amzwaru n tflwit talugaritmiyt (tmzaray f talli nssn).

Tettyawskar tazmilt n ulugaritm zɣ dar [[Grégoire de Saint-Vincent d Alphonse Antonio de Sarasa]] ɣ usggʷas n 1649.

== Isnmal ==
Ad tili <math>a \in ]0 ; + \infty[ </math>, nzḍar ad nini mas d asnml n tsɣnt talugaritmiyt iga tt unrar lli illan ɣ izddar n tsɣnt n <math>x \mapsto 1/x</math> gr <math>a</math> d 1.  Ar tt nttara s tɣarast ad:
[[Afaylu:Log-pole-x 1.svg|thumb|Tasɣnt talugaritm tga unrar lli illan ɣ izddar n tasɣnt <math>x \mapsto 1/x
 </math> gr <math>a
 </math> d 1.]]
<math>\ln a = \int_1^a \frac{1}{x}\,dx.
 </math>

Iɣ darnɣ <math>a<1 </math> rad nini mas d anrar lli darnɣ illan iga uzdir.

Tṭṭaf tasɣnt talugaritmiyt aydatn kullu tn n [[Tasɣnt talugaritmt|tsɣnin tilugaritmin]].<ref>https://www.britannica.com/science/logarithm ''Encyclopedia Britannica''. Tettuyẓra ass n 2020-08-29.</ref>

<math display="inline">\ln(ab) = \ln a + \ln b.

 </math>

Nzḍar ad nml ayad s tibḍit n uɣrd lli f nsawl ɣ umzwaru s snat tfulin ɣ akud ann nɣrd s usnfl n umutti <math>x = ta</math> ɣ tfult tiss snat, zun d mk ad:

<math>\begin{align}
\ln(ab)= \int_1^{ab}\frac{1}{x} \, dx
&=\int_1^a \frac 1 x \, dx + \int_a^{ab} \frac{1}{x} \, dx\\[5pt]
&=\int_1^a \frac 1 x \, dx + \int_1^b \frac{1}{at} \, d(at)\\[5pt]
&=\int_1^a \frac 1 x \, dx + \int_1^b \frac{1}{t} \, dt\\[5pt]
&= \ln a + \ln b.
\end{align}
 </math>

== Aydatn ==
[[Afaylu:Log (2).svg|thumb|264x264px|Tasɣnt n ulugaritm agaman]]

==== Taɣlalt d tsbk n tasɣnt n ulugaritm agaman ====
Zɣ aylli izrin ar nttafa mas d tasɣnt <math>x \mapsto ln(x) </math> tlla ɣar ɣ uzilal <math>]0 ; + \infty[  </math> , nzḍar ad tt nzllm ɣ ammas n uzilal ad nit d:

<math>\forall x \in \R^*_+,\ \ln'(x) = \frac 1x </math>

S ɣikAd tilia <math>ln </math> tasɣnt tamaɣlalt ɣ uzilal <math>]0 ; + \infty[  </math>, acku tazllumt nns tga tumnigt rad nini ma sd <math>ln </math> tga tasɣnt igmmn ɣ ammas uzilal <math>]0 ; + \infty[  </math>

==== Timhal f tasɣnt n ulugaritm agaman ====
Ad tg <math>f </math> yat tsɣnt <math>\ f(x) = \ln(ax)</math> s <math>a </math> d <math>x </math> sin imḍann umnign. Tazllumt nns tga tazllumt nit n ulugaritm agaman, ilmma:

<math>\ f(x) = \ln(x)+k \ / \ k \in \ R</math>

Acku <math display="inline">f(1) =k </math> rad nini mas d <math>ln(a)=k </math> , s yat tɣarast igan tamatayt:

* <math>\forall (a;b)\in ]0 : + \infty[^2,\ \ln(ab) = \ln(a) + \ln(b)</math>

Zɣ uyda yad rad naf aydatn ddaw as:

* <math>\forall (a;b)\in ]0 : + \infty[^2,\ \ln\left(\frac ab\right) = \ln(a) - \ln(b)</math>

Iɣ iga <math>n </math> amḍan waxiḍ:

* <math>\forall a \in ]0 ; + \infty[,\ \forall n \in \Z,\ \ln(a^n) = n \ln(a)</math>
* <math>\forall a \in ]0 ; + \infty[,\ \forall r \in \Q,\ \ln(a^r) = r \ln(a)</math>

Iɣ iga <math>n </math> amḍan ana:

* <math>\forall a \in \R^* ,\ \forall \; n \in \Z^*,\ \ln (a^{n}) = 2n \ln |a| </math>
* <math>\forall (a_1,a_2,....,a_k) \in ]0 : + \infty[^k,\ \sum_{n = 1}^{k}\ln(a_n)= \ln(\prod_{n=1}^k a_n) </math>

<math>\prod</math> ad igan tamatart n ufaris.

==== Aydatn yaḍnin ====
* <math>\ln 1 = 0</math>
* <math>\ln e = 1</math>
* <math>\ln(xy) = \ln x + \ln y \quad \text{i }\; x > 0\;\text{d }\; y > 0</math>
* <math>\ln(x^y) = y \ln x \quad \text{i }\; x > 0</math>
* <math>\ln x < \ln y \quad\text{i }\; 0 < x < y</math>
* <math>\lim_{x \to 0} \frac{\ln(1+x)}{x} = 1</math>
* <math>\lim_{\alpha \to 0} \frac{x^\alpha-1}{\alpha} = \ln x\quad \text{i }\; x > 0</math>
* <math>\frac{x-1}{x} \leq \ln x \leq x-1 \quad\text{i}\quad x > 0</math>
* <math>\ln{( 1+x^\alpha )} \leq \alpha x \quad\text{i}\quad x \ge 0\;\text{d }\; \alpha \ge 1</math>
== Amawal ==
<div style="column-count:4;-moz-column-count:3;-webkit-column count:">
*Agaman : naturel
*Tasɣnt, Tawwuri : fonction
*Afaris : produit
*Timrnit : somme
*Azadur : base
*Tamnzut : fonction primitive
*Azilal : intervalle
*Amusnak : mathematicien
*Taflwit : tableau
*Tazmilt : notion
*Asnml : definition
*Anrar : aire
*Ayda : propriete
*Aɣrd : integrale
*Tafult : partie
*Amutti : variable
*Taɣlalt : continuite
*Uzdir : negatif
*Tsbk : monotonie
*Zllm : deriver
*Igmmn : croissante
*Umnig : positif
*Tamhlt : opperation
*Amḍan : nombre
*Amatay : general
*Waxiḍ : impair
*Ana : paire
</Div>

== Isaɣuln == 
<references/> 
 {{Iɣbula}} 
  
 
 

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