Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 1345

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\[1)\ 5^{2x + 5} \bullet 7^{3x + 1} = 35^{\frac{1}{2}(5x + 6)}\]

\[5^{2x + 5} \bullet 7^{3x + 1} = (5 \bullet 7)^{2,5x + 3}\]

\[\frac{5^{2,5x + 3} \bullet 7^{2,5x + 3}}{5^{2x + 5} \bullet 7^{3x + 1}} = 1\]

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

\[\frac{5^{0,5x}}{7^{0,5x}} \bullet \frac{7^{2}}{5^{2}} = 1\]

\[\frac{5^{0,5x}}{7^{0,5x}} = \frac{5^{2}}{7^{2}}\]

\[0,5x = 2\]

\[x = 4.\]

\[Ответ:\ \ x = 4.\]

\[2)\ {0,2}^{x^{2}} \bullet 5^{2x + 2} = \left( \frac{1}{5} \right)^{6}\]

\[\left( \frac{1}{5} \right)^{x^{2}} \bullet 5^{2x + 2} = 5^{- 6}\]

\[5^{- x^{2}} \bullet 5^{2x + 2} = 5^{- 6}\]

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

\[x^{2} - 2x - 8 = 0\]

\[D = 4 + 32 = 36\]

\[x_{1} = \frac{2 - 6}{2} = - 2;\]

\[x_{2} = \frac{2 + 6}{2} = 4.\]

\[Ответ:\ \ x_{1} = - 2;\ \ x_{2} = 4.\]