Đáp án:
$\begin{array}{l}
+ ){4^{\frac{1}{x}}} + {6^{\frac{1}{x}}} = {9^{\frac{1}{x}}}\\
\Leftrightarrow {\left( {\frac{4}{9}} \right)^{\frac{1}{x}}} + {\left( {\frac{6}{9}} \right)^{\frac{1}{x}}} - 1 = 0\\
\Leftrightarrow {\left( {\frac{2}{3}} \right)^{2.\frac{1}{x}}} + {\left( {\frac{2}{3}} \right)^{\frac{1}{x}}} - 1 = 0\\
\Leftrightarrow {\left( {\frac{2}{3}} \right)^{\frac{1}{x}}} = \frac{{\sqrt 5 - 1}}{2}\left( {do{{\left( {\frac{2}{3}} \right)}^{\frac{1}{x}}} > 0} \right)\\
\Leftrightarrow \frac{1}{x} = 1,186\\
\Rightarrow x = 0,842\\
+ ){3^{{4^x}}} = {4^{{3^x}}}\\
\Rightarrow {81^x} = {64^x}\\
\Rightarrow {\left( {\frac{{81}}{{64}}} \right)^x} = 1\\
\Rightarrow x = 0
\end{array}$
