ln.py

Created by maxime-rigotti

Created on October 16, 2022

634 Bytes

ln(1)=0
(lnx),=1
,=derivee

ln(sqrta*sqrta)=lna
lnsqrta+lnsqrta=lna
2lnsqrta=lna
lnsqrta=1/2lna

ln1/a=lna
lna/b=lna-lnb
lna**n=nlna
lnsqrta=1/2lna
lnab=lna+lnb
lna=lnb<=>a=b
lna<lnb<=>a<b
lne=1

exemples
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=-5x1
lnx=-5lne
lnx=-lne**5
lnx=ln(1/e**5)
x=1/e**5
x=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

lne**2=2lne=2x1=2
lnsqrte=1/2
ln1/sqrte=-lnsqrte=1/2lne=1/2
(lnx)**2-ln(x)-6=0

lnx+ln(x+2)=ln(9x+12)
ln[x(x+2)]=ln(9x-12)
x(x+2)=9x-12
x**2+2x=9x-12
x**2-7x+12=0
X1=4  X2=3
S{4;3}

0=x**2-6x+9  (x+3)**2=0
x=3

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