Question

log(x-2) + log(x+5) = 2log3 . Qual o valor de x?

Answer 1

A resposta está em anexo. Tenha um bom dia, abraço! :)

Answer 2

$log\ (x-2)+log\ (x+5) = 2\ log\ 3\\\\ log\ (x-2)(x+5) = log\ 3^2\\\\\ (x-2)(x+5) = 9\\\\ x^2+5x-2x-10-9=0\\\\\ x^2+3x-19=0\\\\ \Delta = 9+76\\\\ \Delta = 85$

$x^1 = \frac{-3+ \sqrt{85} }{2} \\\\\ x^2 = \frac{-3- \sqrt{85} }{2} \\\\\ \boxed{S(\frac{-3+ \sqrt{85} }{2} ,\frac{-3-\sqrt{85} }{2} )}}$