Задача 18. Решите уравнение \(\lg \left( {{x^2} + 5x} \right) = \lg \left( {{x^2} + 6} \right)\)
Решение
\(\lg \left( {{x^2} + 5x} \right) = \lg \left( {{x^2} + 6} \right)\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{{x^2} + 5x = {x^2} + 6,}\\{{x^2} + 6 > 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,} \right.\left\{ {\begin{array}{*{20}{c}}{x = 1,2,}\\{x\, \in \,R\,\,\,\,\,}\end{array}\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,x = 1,2.} \right.\)
Ответ: 1,2.