2.log cơ số 6 cua(\sqrt[4]{x} +\sqrt[8]{x}) =log cơ số 4 cua (\sqrt[1]{x}
\[\begin{array}{l}
2{\log _6}\left( {\sqrt[4]{x} + \sqrt[8]{x}} \right) = {\log _4}\left( {\sqrt x } \right)\\
dk,x > 0\\
dat:a = 2{\log _6}\left( {\sqrt[4]{x} + \sqrt[8]{x}} \right) = {\log _4}\left( {\sqrt x } \right)\\
\to \left\{ \begin{array}{l}
\sqrt[4]{x} + \sqrt[8]{x} = {6^{\frac{a}{2}}}\\
\sqrt x = {4^a} \to x = {4^{2a}}
\end{array} \right.\\
\to {4^{\frac{a}{2}}} + {4^{\frac{a}{4}}} = {6^{\frac{a}{2}}} \leftrightarrow {\left( {\frac{2}{3}} \right)^{\frac{a}{2}}} + {\left( {\frac{2}{3}} \right)^{\frac{a}{4}}}*\frac{1}{{{6^{\frac{a}{4}}}}} = 1(2)\\
\leftrightarrow f(a) = {\left( {\frac{2}{3}} \right)^{\frac{a}{2}}} + {\left( {\frac{2}{3}} \right)^{\frac{a}{4}}}*\frac{1}{{{6^{\frac{a}{4}}}}}\\
f(2) = 1\\
f(a),ngich,bien\\
\to (2) \leftrightarrow a = 2 \leftrightarrow x = 256
\end{array}\]
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