Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 683

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\[1)\ 5^{x} = 8^{x}\]

\[\frac{5^{x}}{8^{x}} = 1\]

\[\left( \frac{5}{8} \right)^{x} = \left( \frac{5}{8} \right)^{0}\]

\[x = 0\]

\[Ответ:\ \ x = 0.\]

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

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

\[\left( \frac{3}{2} \right)^{x} = \left( \frac{3}{2} \right)^{0}\]

\[x = 0\]

\[Ответ:\ \ x = 0.\]

\[3)\ 3^{x} = 5^{2x}\]

\[\frac{3^{x}}{5^{2x}} = 1\]

\[\left( \frac{3}{5^{2}} \right)^{x} = \left( \frac{3}{5^{2}} \right)^{0}\]

\[x = 0\]

\[Ответ:\ \ x = 0.\]

\[4)\ 4^{x} = 3^{\frac{x}{2}}\]

\[4^{x} = \sqrt{3^{x}}\]

\[\frac{4^{x}}{\sqrt{3^{x}}} = 1\]

\[\left( \frac{4}{\sqrt{3}} \right)^{x} = \left( \frac{4}{\sqrt{3}} \right)^{0}\]

\[x = 0\]

\[Ответ:\ \ x = 0.\]