Задача 18. Найдите корень уравнения \({\log _6}\left( {16-4x} \right)-{\log _6}7 = {\log _6}\dfrac{1}{{35}}\).
Решение
\({\log _6}\left( {16-4x} \right)-{\log _6}7 = {\log _6}\dfrac{1}{{35}}\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\,{\log _6}\dfrac{{16-4x}}{7} = {\log _6}\dfrac{1}{{35}}\,\,\,\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,\,\dfrac{{16-4x}}{7} = \dfrac{1}{{35}}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,16-4x = \dfrac{1}{5}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,-4x = -15,8\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,x = 3,95.\)
Ответ: 3,95.