Решить уровнение log2(2x-6)=4-log2(x-6)

[latex]log_2(2x-6)=4-log_2(x-6)[/latex] [latex]log_2(2x-6)=4log_2(2)-log_2(x-6)[/latex] [latex]log_2(2x-6)=log_2(2^4)-log_2(x-6)[/latex] [latex]log_2(2x-6)=log_2(\frac{2^4}{x-6})[/latex] [latex] \left \{ {{2x-6=\frac{2^4}{x-6}} \atop {x\ \textgreater \ 6}} \right.; \left \{ {{(2x-6)(x-6)=16} \atop {x\ \textgreater \ 6}} \right.; \left \{ {{2x^2-18x+36=16} \atop {x\ \textgreater \ 6}} \right.; \left \{ {{x^2-9x+10=0} \atop {x\ \textgreater \ 6}} \right.;[/latex] [latex]D=(-9)^2-4*10=41[/latex] [latex] \left \{ {{x_{1,2}= \frac{9\pm \sqrt{41} }{2} } \atop {x\ \textgreater \ 6}} \right.;x= \frac{9+\sqrt{41} }{2}[/latex] Ответ: [latex]\frac{9+\sqrt{41} }{2}[/latex]