Профиль №15. Показательные неравенства. Задача 21А

ОТВЕТ: \(\left( {-\infty ;2} \right).\)

\(49 \cdot {4^x}-16 \cdot {7^x} > 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{7^2} \cdot {4^x} > {4^2} \cdot {7^x}\left| {:\left( {{7^2} \cdot {7^x} > 0} \right)\,\,\,\,\,\,\, \Leftrightarrow } \right.\)

\( \Leftrightarrow \,\,\,\,\,\,\,\dfrac{{{4^x}}}{{{7^x}}} > \dfrac{{{4^2}}}{{{7^2}}}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{\left( {\dfrac{4}{7}} \right)^x} > {\left( {\dfrac{4}{7}} \right)^2}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x < 2\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x\, \in \,\left( {-\infty ;2} \right).\)

Ответ:  \(\left( {-\infty ;2} \right).\)