Простейшие логарифмические уравнения. Задача 9

ОТВЕТ: 7.

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

\({\log _x}49 = 2\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{\log _x}{7^2} = 2\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,2{\log _x}7 = 2\,\,\,\,\,\,\, \Leftrightarrow \)

\( \Leftrightarrow \,\,\,\,\,\,\,{\log _x}7 = 1\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{x^1} = 7\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x = 7.\)

Ответ:  7.