Question

$log_{3}x^2-log_{3} ( frac{x}{x+6} )=3$

Answer 1

$log_3x^2-log_3 frac{x}{x+6} =3$
ОДЗ: $left { {{x>0} atop { frac{x}{x+6}>0 }} right.$
$log_3x^2=3+log_3 frac{x}{x+6} \ log_3x^2=log_3frac{27x}{x+6} \ x^2=frac{27x}{x+6} \ x^2(x+6)=27x \ x^2(x+6)-27x=0 \ x(x(x+6)-27)=0 \ x_1=0 \ x^2+x-27=0 \ x_2=-9\ x_3=3$

Ответ: -9 и 3.