Question

log7 (×+2) + log7 (×-3)= log7 14 ?

Answer 1

$log_7(x+2)+log_7(x-3)=log_714\\\\ log_7(x+2)(x-3)=log_714\\\\ (x+2)(x-3)=14\\\\ x^2-3x+2x-6=14\\\\ x^2-x-20=0\\\\ \Delta=(-1)^2-4.1.(-20)=1+80=81\\\\ x=\frac{-(-1)\pm\sqrt{81}}{2.1}\\\\ x=\frac{1\pm9}{2}\\\\ x_1=\frac{1+9}{2}=\frac{10}{2}=5\\\\ x_2=\frac{1-9}{2}=\frac{-8}{2}=-4 \ \ (esse \ valor \ n\~ao \ satisfaz)\\\\ x=5$