Решите неравенство

$Log_x( \sqrt{x^2+x-2}+1)*Log_7(x^2+x+1)=Log_x3$

$ODZ: \left \{ {{ \sqrt{x^2+x-2}+1\ \textgreater \ 0} \atop {x^2+x+1\ \textgreater \ 0}}\atop {x^2+x-2\ \textgreater \ 0; x\ \textgreater \ 0}}}} \right.$

$ODZ: x\ \textgreater \ 1$

$Log_x( \sqrt{x^2+x-2}+1)* \frac{Log_x(x^2+x+1)}{Log_x7})=Log_x3$

$Log_x( \sqrt{x^2+x-2} +1)*Log_x(x^2+x+1)=Log_x3*Log_x7$

$\left \{ {{ \sqrt{x^2+x-2}+1=3} \atop {x^2+x+1=7}} \right. \left \{ {{x^2+x-2=4} \atop {x^2+x-6=0}} \right. \left \{ {{x^2+x-6=0} \atop {x^2+x-6=0} \right. x_1=2; x_2=-3$

т.к. x=-3 не подходит ОДЗ

Ответ х=2

$\left \{ {{ \sqrt{x^2+x-2}+1=7} \atop {x^2+x+1=3}} \right. \left \{ {{x^2+x-2=36} \atop {x^2+x-2=0}} \right.$

общих решений нет

Ответ х=2