Question

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

Answer 1

$log_2(2x-6)=4-log_2(x-6)$

$log_2(2x-6)=4log_2(2)-log_2(x-6)$

$log_2(2x-6)=log_2(2^4)-log_2(x-6)$

$log_2(2x-6)=log_2(\frac{2^4}{x-6})$

$\left \{ {{2x-6=\frac{2^4}{x-6}} \atop {x\ \textgreater \ 6}} \right.; \left \{ {{(2x-6)(x-6)=16} \atop {x\ \textgreater \ 6}} \right.; \left \{ {{2x^2-18x+36=16} \atop {x\ \textgreater \ 6}} \right.; \left \{ {{x^2-9x+10=0} \atop {x\ \textgreater \ 6}} \right.;$

$D=(-9)^2-4*10=41$

$\left \{ {{x_{1,2}= \frac{9\pm \sqrt{41} }{2} } \atop {x\ \textgreater \ 6}} \right.;x= \frac{9+\sqrt{41} }{2}$

ответ: $\frac{9+\sqrt{41} }{2}$