Простейшие логарифмические уравнения. Задача 10

ОТВЕТ: 3.

ОДЗ:  \(\left\{ {\begin{array}{*{20}{c}}{x > 0,}\\{x \ne 1}\end{array}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x\, \in \,\left( {0;1} \right) \cup \left( {1;\infty } \right).} \right.\)

\({\log _x}\dfrac{1}{{27}} = -3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{\log _x}{3^{-3}} = -3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,-3{\log _x}3 = -3\,\,\,\,\,\,\, \Leftrightarrow \)

\( \Leftrightarrow \,\,\,\,\,\,\,{\log _x}3 = 1\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{x^1} = 3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x = 3.\)

Ответ:  3.