Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 497

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\[1)\ 6^{3x} = 6^{4}\]

\[3x = 4\]

\[\ x = \frac{4}{3} = 1\frac{1}{3}.\]

\[Ответ:\ \ x = 1\frac{1}{3}.\]

\[2)\ \left( \frac{2}{3} \right)^{2x} = \left( \frac{2}{3} \right)^{- 3}\]

\[2x = - 3\]

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

\[x = - 1,5.\]

\[Ответ:\ \ x = - 1,5.\]

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

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

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

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

\[Ответ:\ \ x = \sqrt{2}.\]

\[4)\ 32^{x} = 2^{10}\]

\[\left( 2^{5} \right)^{x} = 2^{10}\]

\[5x = 10\]

\[x = 2.\]

\[Ответ:\ \ x = 2.\]