\(\begin{array}{l}
Cau\,\,25:\\
{x^2} + 4{y^2} = 12xy\\
\Leftrightarrow {x^2} + 4xy + 4{y^2} = 16xy\\
\Leftrightarrow {\left( {x + 2y} \right)^2} = 16xy\\
\Rightarrow {\log _2}{\left( {x + 2y} \right)^2} = {\log _2}16xy\\
\Leftrightarrow 2{\log _2}\left( {x + 2y} \right) = {\log _2}16 + {\log _2}x + {\log _2}y\\
\Leftrightarrow 2{\log _2}\left( {x + 2y} \right) = 4 + {\log _2}x + {\log _2}y\\
\Leftrightarrow {\log _2}\left( {x + 2y} \right) = 2 + \frac{1}{2}\left( {{{\log }_2}x + {{\log }_2}y} \right).
\end{array}\)
