Простейшие показательные уравнения. Задача 18

ОТВЕТ: 1,5.

\(27 \cdot {4^x}-8 \cdot {9^x} = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{3^3} \cdot {2^{2x}} = {2^3} \cdot {3^{2x}}\left| {:{3^3} \cdot {3^{2x}} \ne 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,} \right.\)

\( \Leftrightarrow \,\,\,\,\,\,{\left( {\dfrac{2}{3}} \right)^{2x}} = {\left( {\dfrac{2}{3}} \right)^3}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,2x = 3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x = 1,5.\,\)

Ответ:  1,5.