Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 210

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\[1)\ 3 \bullet 9^{x} = 81\]

\[3 \bullet 3^{2x} = 3^{4}\]

\[3^{1 + 2x} = 3^{4}\]

\[1 + 2x = 4\]

\[2x = 3\]

\[x = 1,5\]

\[Ответ:\ \ x = 1,5.\]

\[2)\ 2 \bullet 4^{x} = 64\]

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

\[2^{1 + 2x} = 2^{6}\]

\[1 + 2x = 6\]

\[2x = 5\]

\[x = 2,5\]

\[Ответ:\ \ x = 2,5.\]

\[3)\ 3^{x + \frac{1}{2}} \bullet 3^{x - 2} = 1\]

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

\[3^{x + \frac{1}{2}} = 3^{- (x - 2)}\]

\[x + \frac{1}{2} = - (x - 2)\]

\[x + 0,5 = 2 - x\]

\[2x = 1,5\]

\[x = 0,75\]

\[Ответ:\ \ x = 0,75.\]

\[4)\ {0,5}^{x + 7} \bullet {0,5}^{1 - 2x} = 2\]

\[{0,5}^{x + 7 + 1 - 2x} = \left( \frac{1}{2} \right)^{- 1}\]

\[{0,5}^{8 - x} = {0,5}^{- 1}\]

\[8 - x = - 1\]

\[- x = - 9\]

\[x = 9\]

\[Ответ:\ \ x = 9.\]

\[5)\ {0,6}^{x} \bullet {0,6}^{3} = \frac{{0,6}^{2x}}{{0,6}^{5}}\]

\[{0,6}^{x + 3} = {0,6}^{2x - 5}\]

\[x + 3 = 2x - 5\]

\[- x = - 8\]

\[x = 8\]

\[Ответ:\ \ x = 8.\]

\[6)\ 6^{3x} \bullet \frac{1}{6} = 6 \bullet \left( \frac{1}{6} \right)^{2x}\]

\[\frac{6^{3x}}{6^{1}} = \frac{6^{1}}{6^{2x}}\]

\[6^{3x - 1} = 6^{1 - 2x}\]

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

\[5x = 2\]

\[x = 0,4\]

\[Ответ:\ \ x = 0,4.\]