Đáp án:
$\begin{array}{l}
4{\log _{25}}x + {\log _5}x = 3\\
\Rightarrow 2.{\log _5}x + {\log _5}x = 3\\
\Rightarrow {\log _5}x = 1\\
\Rightarrow x = 5\\
4{\log _{25}}x + {\log _x}5 = 3\\
\Rightarrow 2.{\log _5}x + {\log _x}5 = 3\\
\Rightarrow 2{\log _5}x + \dfrac{1}{{{{\log }_5}x}} = 3\\
Dat:{\log _5}x = t\left( {t \ne 0} \right)\\
\Rightarrow 2t + \dfrac{1}{t} = 3\\
\Rightarrow 2{t^2} - 3t + 1 = 0\\
\Rightarrow \left( {2t - 1} \right)\left( {t - 1} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
t = \dfrac{1}{2}\left( {tm} \right)\\
t = 1\left( {tm} \right)
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
{\log _5}x = \dfrac{1}{2}\\
{\log _5}x = 1
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = \sqrt 5 \\
x = 5
\end{array} \right.
\end{array}$
