# Ejercicios de logaritmos, resueltos y desarrollados

Páginas: 2 (417 palabras) Publicado: 18 de octubre de 2010
EJERCICIOS CON LOGARITMOS
GABRIELA TELLEZ TERRAZAS GRUPO: 518
4x+2x+3=48
22x+2x23=48
2x2+82x=48
Sea Y= 2x
y²+8y-48=0
(Y +12)(y-4)=0
Y1=-12
Y2=4
2x= 4
X=42X=2
COMPROBACION
4²+22+3=48
16+32=48
48=48

Log(x-2) + Log x= Log 8
Log x(x-2)=Log8
X(x-2)=8
X²-2x-8=0
(x-4)(X+2)=0
X=4
COMPROBACION
Log (4-2)+log4=log8Log2+log4=log8
0.30102+0.60205=0.90308
0.90308=0.90308

Log(x-5) + log(x+4)=1
Log (x -5) (x+4)=1
Log (x-5) (x+4)=log 10
(x-5)(x-4)=10
X² -x-20=10
X²-x-30=0
(x-6)(X+5)=0X=6
COMPROBACION
Log (6-5)+log (6+4)=1
Log1+log10=1
0+1=1
1=1

Log(x²-15x)=3
Log(x²-15x)=log1000
X²-15x=1000
X²-15x-1000=0
(x-40)(X+25)=0
X=40
COMPROBACION
Log(40²-15(40))=3
Log1000=3
3=3

logx+log(x-3)=1
Log x(x-3)=log10
X(x-3)=10
X²-3x-10
(X+2)(x-5)=0
X=5
COMPROBACION
Log5+log (5-3)=1
0.69897+0.30102=1
1=12logx-log(x+6)=3log2
Logx²-log(x+6)=log2³
logx2x+6=log2³
x2x+6=8
X²=8x+48
X²-8x-48
(X+4)(x-12)
X=12
COMPROBACION
2log12-log (12+6)=3log2
2log12-log18=3log22.158362-1.255272=0.90308
0.90308=0.90308

2logx-log(x-16)=2
Logx²-log(x-16)=log100
logx2x-16=log100
x2x-16=100
X²=100x-1600
X²-100x+1600=0
X1=20
X2=80
COMPROBACION
2log20-log(20-16)=2
2.60205-0.60205=2
2=2

logx³=log6+logx
logx³=log (6x)
X³=6x
X³-6x=0
X(x²-6)=0
X=±√6
COMPROBACION
Log±6 ³ = log6+log±6
1.167226876=0.7781512504+0.389075625211.167226876=1.167226876

Log (3x-1)-log (2x+3)=1-log25
Log 3x-12x+3=log10-log25
Log3x-12x+3=log1025

3x-12x+3=1025

3x-12x+3=25

5(3x-.1)= 2(2x+3)
15x-5=4x+6
X=1COMPROBACION
Log (3(1)-1)-log (2(1)+3)=1-log25
Log2-log5=1-log25
0.30102-0.69897=1-1.39794
-0.39794=-0.39794

2x=57
Log2x=log57
xlog2=log57
x=log57log2
X=5.832890014

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