Log4(x^2+x)=log 4(x^2+9)

{х² + х = х² + 9, {x² + x > 0, {x = 9, {[x < -1, {[x > 0, Ответ: 9.

[latex]log_4(x^2+x)=log_4(x^2+9)[/latex] ОДЗ: [latex] \left \{ {{x^2+x\ \textgreater \ 0} \atop {x^2+9\ \textgreater \ 0}} \right. ~~~ \left \{ {{x(x+1)\ \textgreater \ 0} \atop {x^2+9\ \textgreater \ 0}} \right. ~~~x\in(-\infty;-1) \text{ U }(0;+\infty)[/latex] Решение: [latex]log_4(x^2+x)=log_4(x^2+9) \\ x^2+x=x^2+9 \\ x=9[/latex] Ответ: 9