logexpo.py

Created by maxime-rigotti

Created on November 20, 2022

644 Bytes

  ln(x)
(lnx)"=1
ln(1)=0
ln1/a=-lna
lna**n=nlna
ln(sqrta*sqrta)=lna
lnsqrta+lnsqrta=lna
2lnsqrta=1/2lna
lna/b=lna-lnb
lnsqrta=1/2lna
lne=1

  exemple
ln(x+2)=2lnx
ln(x+2)=lnx**2
x+2=x**2
0=x**2-2-x
X1=-1  X2=2
S={2}

lnx=-5
lnx=-5*1
lnx=-5lne
lnx=-lne**5
lnx=ln1/e**5
x=1/e**5=e-5

ln(3x+1)-ln(x+1)>ln2
ln(3x+1)>ln2+ln(x+1)
3x+1>2(x+1)
3x+1>2x+2
x>1
S={1;+infini}

lne-1=-lne-1
lne2=2lne=2*1=2
lnsqrte=1/2
ln1/sqrte=-lnsqrte=1/2lne=-1/2


  exponentiel
ea+b=ea*eb
ea-b=ea/eb
(ea**n)=en*a
ex>0
elnx=lnex=x
e-a=1/ea

  exemples
eln3=3  e1/2ln3=sqrt3  e-ln2=eln1/2=1/2
ln1/e=-lne=-1  e-2ln3=eln3**-2=1/3**2=1/9

ex=3
lnex=ln3
x=ln3

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