Respuestas

  • Usuario de Brainly
2013-12-09T04:09:06+01:00
log(x+2)+log(x-1)=

Ojo: x+2 >0     ^   x-1>0
      x>-2              x>1
Intersectando:  x>1


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

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

(x+2)(x-1) = 10¹

x² + x  - 2 = 10

x² + x -12 =0

x² + 4x - 3x - 12 =0

x(x+4) -3(x+4)=0

(x-3)(x+4)=0

=> x-3=0                 ó           x + 4 =0
       x =3                               x = -4

Pero: x>1  , por lo tanto x=3


Comprobando:

log(3+2) + log(3-1)=1

log(5) + log(2) =1

log(10) = 1

10 = 10