Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 209

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\[1)\ 27^{x} = \frac{1}{3}\]

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

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

\[3x = - 1\]

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

\[Ответ:\ \ x = - \frac{1}{3}.\]

\[2)\ 400^{x} = \frac{1}{20}\]

\[\left( 20^{2} \right)^{x} = 20^{- 1}\]

\[20^{2x} = 20^{- 1}\]

\[2x = - 1\]

\[x = - \frac{1}{2}\]

\[Ответ:\ \ x = - 0,5.\]

\[3)\ \left( \frac{1}{5} \right)^{x} = 25\]

\[\left( 5^{- 1} \right)^{x} = 5^{2}\]

\[5^{- x} = 5^{2}\]

\[- x = 2\]

\[x = - 2\]

\[Ответ:\ \ x = - 2.\]

\[4)\ \left( \frac{1}{3} \right)^{x} = \frac{1}{81}\]

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

\[x = 4\]

\[Ответ:\ \ x = 4.\]