Решите неравенство [latex] log_{x} (\sqrt{x^{2}+x-2 }+1)* log_{7}( x^{2}+x+1)= log_{x}3 [/latex]

[latex]Log_x( \sqrt{x^2+x-2}+1)*Log_7(x^2+x+1)=Log_x3 [/latex] [latex]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. [/latex] [latex]ODZ: x\ \textgreater \ 1[/latex] [latex]Log_x( \sqrt{x^2+x-2}+1)* \frac{Log_x(x^2+x+1)}{Log_x7})=Log_x3 [/latex] [latex]Log_x( \sqrt{x^2+x-2} +1)*Log_x(x^2+x+1)=Log_x3*Log_x7 [/latex] [latex] \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 [/latex] т.к. x=-3 не подходит ОДЗ Ответ х=2 [latex] \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. [/latex] общих решений нет Ответ х=2