[latex]log_{3}x^2-log_{3} ( \frac{x}{x+6} )=3[/latex]

[latex]\log_3x^2-\log_3 \frac{x}{x+6} =3[/latex] ОДЗ: [latex] \left \{ {{x>0} \atop { \frac{x}{x+6}>0 }} \right. [/latex] [latex]\log_3x^2=3+\log_3 \frac{x}{x+6} \\ \log_3x^2=\log_3\frac{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[/latex] Ответ: -9 и 3.