Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 84

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\[1)\ 5^{2x} = 5^{4}\]

\[2x = 4\ \]

\[x = \frac{4}{2}\]

\[x = 2\]

\[Ответ:\ \ x = 2.\]

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

\[2x = - 1\]

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

\[x = - 0,5\]

\[Ответ:\ \ x = - 0,5.\]

\[3)\ 9^{x} = 3^{2\sqrt{2}}\]

\[9^{x} = \left( 3^{2} \right)^{\sqrt{2}}\]

\[9^{x} = 9^{\sqrt{2}}\]

\[x = \sqrt{2}\]

\[Ответ:\ \ x = \sqrt{2}.\]

\[4)\ 16^{x} = 2^{8\pi}\]

\[\left( 2^{4} \right)^{x} = 2^{8\pi}\]

\[2^{4x} = 2^{8\pi}\]

\[4x = 8\pi\ \]

\[x = \frac{8\pi}{4}\]

\[x = 2\pi\]

\[Ответ:\ \ x = 2\pi.\]