ГДЗ по алгебре и начала математического анализа 10 класс Алимов Задание 1346

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\[1)\ {2,4}^{3 - 2x} = {2,4}^{3x - 2}\]

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

\[- 5x = - 5\]

\[x = 1.\]

\[Ответ:\ \ x = 1.\]

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

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

\[- x = x - 2\]

\[- 2x = - 2\]

\[x = 1.\]

\[Ответ:\ \ x = 1.\]

\[3)\ \frac{1}{\sqrt{8}} = \left( \frac{1}{16} \right)^{- x}\]

\[8^{- \frac{1}{2}} = 16^{- ( - x)}\]

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

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

\[- \frac{3}{2} = 4x\]

\[x = - \frac{3}{8}.\]

\[Ответ:\ \ x = - \frac{3}{8}.\]