Log9 (x+6)=log9 (4x-9)

ОДЗ: [latex] \left \{ {{x+6\ \textgreater \ 0} \atop {4x-9\ \textgreater \ 0}} \right. \Rightarrow \left \{ {{x\ \textgreater \ -6} \atop {x\ \textgreater \ \frac{9}{4} }} \right. \Rightarrow \boxed{x\ \textgreater \ \frac{9}{4}}[/latex] Основания одинаковы, значит            [latex]x+6=4x-9\\ x-4x=-9-6\\ -3x=-15\\ x=5[/latex]