Задача 8. Решите уравнение    \({\log _7}\left( {{x^2} + 5x} \right) = {\log _7}\left( {{x^2} + 6} \right).\)

Ответ

ОТВЕТ: 1,2.

Решение

\({\log _7}\left( {{x^2} + 5x} \right) = {\log _7}\left( {{x^2} + 6} \right)\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{{x^2} + 5x = {x^2} + 6}\\{{x^2} + 6 > 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{x = 1,2}\\{x\, \in \,\,R}\end{array}} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,x = 1,2.\)

Ответ: 1,2.