Задача 15. Найдите корень уравнения \({\log _{0,5}}\left( {2x + 5} \right)-{\log _{0,5}}13 = {\log _{0,5}}5\).
Решение
\({\log _{0,5}}\left( {2x + 5} \right)-{\log _{0,5}}13 = {\log _{0,5}}5\,\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\,\,{\log _{0,5}}\left( {2x + 5} \right) = {\log _{0,5}}5 + {\log _{0,5}}13\,\,\,\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,\,{\log _{0,5}}\left( {2x + 5} \right) = {\log _{0,5}}65\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,2x + 5 = 65\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,2x = 60\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,x = 30.\)
Ответ: 30.