Question

Rezolvati in multimea nr. reale ecuatia log in baza 8 din (x^2-27)=log in baza 8 din (x-3)^2

Answer 1

 

$\displaystyle\\\log_8(x^2-27)=\log_8(x-3)^2\\\\\text{Bazele sunt egale.}\\\\\implies~x^2-27=(x-3)^2\\\\x^2-27=x^2-6x+9~~\Big|~-x^2\\\\-27=-6x+9\\\\6x=9+27\\\\6x=36\\\\x=\frac{36}{6}\\\\\boxed{x=6}$

Answer 2

Explicație pas cu pas:

log in baza 8 din (x^2-27)=log in baza 8 din (x-3)^2

DVA:x∈(3√3,+∞)

x²-27=(x-3)²

x²-x²+6x-9-27=0

6x=36

x=6∈DVA

Bafta!