Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 1347

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\[1)\ \left( \frac{4}{9} \right)^{x} \bullet \left( \frac{27}{8} \right)^{x - 1} = \frac{2}{3}\]

\[\left( \frac{2^{2}}{3^{2}} \right)^{x} \bullet \left( \frac{3^{3}}{2^{3}} \right)^{x - 1} = \frac{2}{3}\]

\[\left( \frac{2}{3} \right)^{2x} \bullet \left( \frac{2}{3} \right)^{- 3(x - 1)} = \frac{2}{3}\]

\[2x - 3(x - 1) = 1\]

\[2x - 3x + 3 = 1\]

\[- x = - 2\]

\[x = 2.\]

\[Ответ:\ \ x = 2.\]

\[2)\ \sqrt[3]{2^{x}} \bullet \sqrt[3]{3^{x}} = 216\]

\[2^{\frac{x}{3}} \bullet 3^{\frac{x}{3}} = 6^{3}\]

\[6^{\frac{x}{3}} = 6^{3}\]

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

\[x = 9.\]

\[Ответ:\ \ x = 9.\]