Простейшие показательные уравнения. Задача 21

ОТВЕТ: 2.

\({4^{x + 1}}-{2^{2x-2}} = 60\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,4 \cdot {2^{2x}}-\dfrac{{{2^{2x}}}}{{{2^2}}} = 60\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{2^{2x}} \cdot \left( {4-\dfrac{1}{4}} \right) = 60\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\)

\( \Leftrightarrow \,\,\,\,\,\,\,{2^{2x}} \cdot \dfrac{{15}}{4} = 60\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{2^{2x}} = 16\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{2^{2x}} = {2^4}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,2x = 2\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x = 2.\)

Ответ:  2.