Question

Rezolvati in multimea numerelor reale ecuatia log in baza 3 din(x+2)-log in baza 3 din (x-4)egal cu 1

Answer 1

[tex]log_3(x+2)-log_3(x-4)=1\\ Conditii \ de \ existenta:\\ x+2\ \textgreater \ 0=\ \textgreater \ x\ \textgreater \ -2\\ x-4\ \textgreater \ 0=\ \textgreater \ x\ \textgreater \ 4\\ Deducem \ x \in(4,+\infty)\\ log_3\frac{x+2}{x-4}=log_33\\ \frac{x+2}{x-4}=3\\ 3(x-4)=x+2\\ 3x-12=x+2\\ 2x=14\\ x=7[/tex]