Question

Rezolvati in multimea numerelor reale ecuatia $log_{3}$ (x-4)=$log_{3}$ (6x-12) .

Answer 1

[tex] log_{3} (x^2-4)= log_{3} (6x-12) log_{3} (x^2-4)= log_{3} (6x-12), [/tex]

unde x∈(2,+∞)

[tex]x^2-4=6x-12 (x-2)(x+2)=6(x-2) (x-2)(x+2)-6(x-2)=0 (x-2)(x+2-6)=0 (x-2)(x-4)=0 \left \{ {{x-2=0} \atop {x-4=0}} \right. x=2 x=4 [/tex]

unde x∈(2,+∞)

deci x=4