ГДЗ по алгебре и начала математического анализа 10 класс Алимов Задание 279

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\[1)\log_{2}\sqrt[4]{2} = \log_{2}2^{\frac{1}{4}} = \frac{1}{4} = 0,25\]

\[2)\log_{3}\frac{1}{3\sqrt{3}} = \log_{3}\frac{1}{3^{1} \bullet 3^{\frac{1}{2}}} =\]

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

\[= - 1,5\]

\[3)\log_{0,5}\frac{1}{\sqrt{32}} = \log_{0,5}\left( \frac{1}{32} \right)^{\frac{1}{2}} =\]

\[= \log_{\frac{1}{2}}\left( \frac{1}{2} \right)^{\frac{5}{2}} = \frac{5}{2} = 2,5\]

\[4)\log_{7}\frac{\sqrt[3]{7}}{49} = \log_{7}\frac{7^{\frac{1}{3}}}{7^{2}} =\]

\[= \log_{7}7^{\frac{1}{3} - 2} = \frac{1}{3} - 2 = \frac{1}{3} - \frac{6}{3} =\]

\[= - \frac{5}{3} = - 1\frac{2}{3}\]