Question

Alguem me ajuda nessa equaçao logaritmica?

Answer 1

Resposta:

Letra A

Explicação passo-a-passo:

Utilizando as propriedades do logaritmo temos:

$log_3(x^2-2x-3)+log_\frac{1}{3}(x-1)=log_3(x+1)\\\\log_3(x^2-2x-3)+log_{3^{-1}} (x-1)=log_3(x+1)\\\\log_3(x^2-2x-3)+(\frac{1}{-1})log_3(x-1)=log_3(x+1)\\\\log_3(x^2-2x-3)-log_3(x-1)=log_3(x+1)\\\\log_3\Big(\dfrac{x^2-2x-3}{x-1}\Big)=log_3(x+1)\\\\\dfrac{x^2-2x-3}{x-1}=(x+1)\\\\x^2-2x-3=(x+1).(x-1)\\x^2-2x-3=x^2-1\\-2x-3=-1\\-2x=-1+3\\-2x=2\\x=\frac{2}{-2}\\x=-1\\\\S=\{-1\}$