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Margauxbsg
@Margauxbsg
April 2019
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SVP urgent : résoudre l'équation suivante :
• ln(x)-ln(1-x) = ln2
en précisant son ensemble de définition ; puis de meme pour l'inéquation :
• ln(x) > e
Je suis complètement perdue sur ce chapitre car j'étais absente, merci d'avance
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caylus
Verified answer
Bonsoir,
Rappels
ln (a/b)=ln (a)-ln(b)
ln(a^n)=n ln(a)
y=ln (x) =>e^y=x
Domaine de définition de ln (a) : a>0
1) ln(x)-ln(1-x) => x>0 et 1-x>0 => 0<x<1
ln(x)-ln(1-x)=ln(2)
=> ln (x/(1-x))=ln (2)
=> x/(1-x)=2
=> x=2-2x
=>3x=2
x=2/3 et 0<2/3<1.
2) ln(x)>e =>x>0
x>e^e
=>x> 15,15426224147926418976043027263.....
0 votes
Thanks 1
margauxbsg
merci beaucoup! j'en ai oublié un dans l'énoncé : e^x-1 < 2
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Verified answer
Bonsoir,Rappels
ln (a/b)=ln (a)-ln(b)
ln(a^n)=n ln(a)
y=ln (x) =>e^y=x
Domaine de définition de ln (a) : a>0
1) ln(x)-ln(1-x) => x>0 et 1-x>0 => 0<x<1
ln(x)-ln(1-x)=ln(2)
=> ln (x/(1-x))=ln (2)
=> x/(1-x)=2
=> x=2-2x
=>3x=2
x=2/3 et 0<2/3<1.
2) ln(x)>e =>x>0
x>e^e
=>x> 15,15426224147926418976043027263.....