Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 197

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\[1)\ y = 2^{x}\text{\ \ }и\ \ y = 8\]

\[2^{x} = 8\]

\[2^{x} = 2^{3}\]

\[x = 3\]

\[Ответ:\ \ (3;\ 8).\]

\[2)\ y = 3^{x}\text{\ \ }и\ \ y = \frac{1}{3}\]

\[3^{x} = \frac{1}{3}\]

\[3^{x} = 3^{- 1}\]

\[x = - 1\]

\[Ответ:\ \ \left( - 1;\ \frac{1}{3} \right).\]

\[3)\ y = \left( \frac{1}{4} \right)^{x}\ и\ \ y = \frac{1}{16}\]

\[\left( \frac{1}{4} \right)^{x} = \frac{1}{16}\]

\[\left( \frac{1}{4} \right)^{x} = \left( \frac{1}{4} \right)^{2}\]

\[x = 2\]

\[Ответ:\ \ \left( 2;\ \frac{1}{16} \right).\]

\[4)\ y = \left( \frac{1}{3} \right)^{x}\ и\ \ y = 9\]

\[\left( \frac{1}{3} \right)^{x} = 9\]

\[3^{- x} = 3^{2}\]

\[- x = 2\]

\[x = - 2\]

\(Ответ:\ \ ( - 2;\ 9).\)