ГДЗ по алгебре и начала математического анализа 10 класс Колягин Задание 772

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\[1)\log_{x}27 = 3\]

\[\log_{x}27 = \log_{x}x^{3}\]

\[27 = x^{3}\]

\[x = \sqrt[3]{27} = 3\]

\[Ответ:\ \ x = 3.\]

\[2)\log_{x}\frac{1}{7} = - 1\]

\[\log_{x}\frac{1}{7} = \log_{x}x^{- 1}\]

\[\frac{1}{7} = x^{- 1}\]

\[\frac{1}{7} = \frac{1}{x}\ \]

\[x = 7\]

\[Ответ:\ \ x = 7.\]

\[3)\log_{x}\sqrt{5} = - 4\]

\[\log_{x}\sqrt{5} = \log_{x}x^{- 4}\]

\[\sqrt{5} = x^{- 4}\]

\[\sqrt{5} = \frac{1}{x^{4}}\]

\[x^{4} = \frac{1}{\sqrt{5}}\]

\[x = \sqrt[4]{\frac{1}{\sqrt{5}}} = \sqrt[4]{5^{- \frac{1}{2}}} =\]

\[= 5^{- \frac{1}{2}\ \ :\ 4} = 5^{- \frac{1}{8}}\]

\[Ответ:\ \ x = 5^{- \frac{1}{8}}.\]

\[4)\log_{x}{0,2} = - 3\]

\[x^{- 3} = \left( \left( \frac{1}{5} \right)^{- \frac{1}{3}} \right)^{- 3}\]

\[x = \left( \frac{1}{5} \right)^{- \frac{1}{3}}\]

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

\[Ответ:\ \ x = 5^{\frac{1}{3}}.\]