Задача 5. Найдите корень уравнения \({\log _4}\left( {3 + x} \right) = \log {}_4\left( {4x — 15} \right).\)
Решение
\({\log _4}\left( {3 + x} \right) = {\log _4}\left( {4x — 15} \right)\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{3 + x = 4x — 15}\\{3 + x > 0\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{x = 6\,\,\,}\\{x > — 3}\end{array}} \right.\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x = 6.\)
Ответ: 6.