Распишите подробно решение: [latex] X^{ log _{3}X-2 } = 27[/latex]

[latex]X^{ log _{3}(x-2) } = 27 \\ \\ log_x(27)=log_3(x-2) \\ \\ \frac{1}{log_{27}(x)} =log_3(x-2) \\ \\ \frac{1}{log_{3^3}(x)} =log_3(x-2) \\ \\ \frac{1}{ \frac{1}{3} log_{3}(x)} =log_3(x-2) \\ \\ \frac{3}{log_3(x)} =log_3(x-2) \\ \\ [/latex] [latex]\frac{3}{x} =x-2 \\ \\ 3=x(x-2) \\ x^2-2x-3=0 \\ D=4-4*(-3)=4+12=16 \\ x_1=3 \\ x_2=-1[/latex]