Простейшие логарифмические уравнения. Задача 33

ОТВЕТ: 3.

\(3{\log _4}x = {\log _4}9 + {\log _4}3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,3{\log _4}x = {\log _4}27\,\,\,\,\,\,\, \Leftrightarrow \)

\( \Leftrightarrow \,\,\,\,\,\,\,3{\log _4}x = {\log _4}{3^3}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,3{\log _4}x = 3{\log _4}3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{\log _4}x = {\log _4}3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x = 3.\)

Ответ:  3.