Простейшие логарифмические уравнения. Задача 30

ОТВЕТ: 1.

\({\log _2}\left( {{x^2} + 7x-5} \right) = {\log _2}\left( {4x-1} \right)\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{{x^2} + 7x-5 = 4x-1,}\\{4x-1 > 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}\,\,\,\,\,\,\, \Leftrightarrow } \right.\)

\( \Leftrightarrow \,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{{x^2} + 3x-4 = 0,}\\{x > 0,25\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,} \right.\left\{ {\begin{array}{*{20}{c}}{\left[ {\begin{array}{*{20}{c}}{x = 1,\,\,\,}\\{x = -4}\end{array}} \right.}\\{x > 0,25}\end{array}} \right.\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x = 1.\)

Ответ:  1.