UNIVERSIDAD CENTRAL DEL ECUADOR

FACULTAD DE FILOSOFA LETRAS Y CIENCIAS DE LA EDUCACIN

CARRERA DE INFORMTICA

Nombres: Miguel Sanango, Alexandra Batalla

Curso: 2do A

Matemtica II

I. Calcula los siguientes logaritmos:

1. log4 64 =

4^x = 64

xlog(4) = log(64)

x = log(64)/log(4)

x = 3

2. log1/3 9 =

1/3^x = 9

xlog(1/3) = log(9)

x = log(9)/log(1/3)

x = -2

3.log (pi0) = 0

4. log16 8 =

16^x = 8 xlog(16) = log(8) x = log(8)/log(16) x = 0.75

5. log125 25 =

125^x = 25 xlog(125) = log(25) x = log(25)/log(125) x = 0.666...

6. log1 5 =

No se puede dividir entre cero. 7. log81 3 =

81^x = 3 xlog(81) = log(3) x = log(3)/log(81) x = 0.25 8. log4 32 - log2 16 =

4^x1 = 32

x1log(4) = log(32)

x1 = log(32)/log(4)

x1 =2.5

2^x2 = 16

x2log(2) = log(16)

x2 = log(16)/log(2)

x2 =4

x1- x2=2.5-4=-1.5 9. logb (bb) =

b^x= bb xlog(b) = log(bb) x = log(bb)/log(b) x = b

II. Resuelve las siguientes ecuaciones logartmicas

1. log(x + 1) = log(2x - 5)

log (x+1) = log (2x -5)

(x+1)=(2x-5)

x-2x=-5-1

-x=-6

X=6

2. log 5 + log(x + 4) = log(x - 8)

log5 +log(x+4) = log (x-8)

log(x+4) *5=log(x-8)

5x+20=x-8

5x-x=-20-8

4x=-28

X=-7

3. log(x + 7) + log(x - 3) = log(x2 + 3)

log(x+7) *(x-3)= log(x2 + 3)

log(x2-3x+7x-21)=log(x2 + 3)

(x2-3x+7x-21)= (x2 + 3)

-3x+7x=21+3

4X=24

X=6

4. log(x + 8) - log(x) = log(3x + 9)

log(x+8) /(x)= log(3x+9)

(x+8) /(x)= (3x+9)

(x+8/x)-3x=9

X+8-3x2=9

-3x2+x-1

3x2-x+1

(1(+-)sqr(1-4(3)(1))/2

=(1(+-)sqr(11))/2

5. log(x + 3) - log(x + 4) = log(x - 7) - log(x - 4)

log(x+4) /(x + 4) =log(x-7)/ (x - 4)

(x+4) /(x + 4) =(x-7)/ (x - 4)

(x2-4x+4x-16)=(x2-4x+7x-28)

3x=12

X=4

6. (log(x))2 - 2 log(x) = -1

x-2x=-1

x-2x+1=0

(x-1)(x-1)=0

X= 1 ; x=1

7. 5(log(x))2 - 2 log(x) = 3

5x-2x=3

5x-2x-3=0

(5x-3)(x+1)=0

x=3/5 ; x=-1

8. log(x + 1) + log(x + 3) = log(x - 2) + log(x - 3)

x+2x+x+3 = x-3x-2x+6

x+4x+3 = x-5x+6

9x = 6-3

X= 3/9

X= 1/3