Question

Resolva a equação:


Log de (x+2) na base 3 + log de (x) na base 3 = 3 - log de 9 na base 3

Answer 1

log₃ (x+2) + log₃x = 3 - log₃ 9

log₃ (x+2) + log₃ x = log₃ 27 - log₃ 9

log₃ (x+2)•x = log₃ (27/9)

(x +2)•x = (3)

x² +2x -3 = 0
∆=4 +12= 16 ==> √∆=4
x = -2±√∆/2a
x' = -2+4/2 = 2/2= 1 ✓
x" = -2-4/2 =-6/2= -3 (não serve)
S : { 1 } ✓

Answer 2

log (x+2) + logx = 3 - log 9

log(x+2).x=3-log9

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

log(x+2).x=1

3^1=x.(x+2)

x.(x+2)=3

x^2+2x-3=0

∆=b^2-4.a.c

∆=(2)^2-4.(1).(-3)

∆=4+12

∆=16

x'=-2+4/2

x'=2/2

x'=1 (serve)

x"=-2-4/2

x"=-6/2

x"=-3 (não serve)


s={1}