Задача 3. Найдите корень уравнения    \({\left( {\frac{1}{4}} \right)^{4x — 10}} = \frac{1}{{16}}.\)

Ответ

ОТВЕТ: 3.

Решение

\({\left( {\frac{1}{4}} \right)^{4x — 10}} = \frac{1}{{16}}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,{\left( {\frac{1}{4}} \right)^{4x — 10}} = {\left( {\frac{1}{4}} \right)^2}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,4x — 10 = 2\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x = 3.\)

Ответ: 3.