Bài giải

${{\log }_{5}}\left( 5x \right)-{{\log }_{25}}\left( 5x \right)-3=0$

$\Leftrightarrow \left\{ \begin{align}& x>0 \\ & {{\log }_{5}}(5x)-\frac{1}{2}{{\log }_{5}}(5x)-3=0 \\ \end{align} \right.$

$\Leftrightarrow \left\{ \begin{align}& x>0 \\ & \frac{1}{2}{{\log }_{5}}(5x)-3=0 \\ \end{align} \right.$

$\Leftrightarrow \left\{ \begin{align}& x>1 \\ & {{\log }_{5}}(5x)=6 \\ \end{align} \right.$

$\Leftrightarrow \left\{ \begin{align}& x>1 \\ & 5x={{5}^{6}} \\ \end{align} \right.$

$\Leftrightarrow \left\{ \begin{align}& x>1 \\ & x={{5}^{5}} \\ \end{align} \right.$ $\Leftrightarrow x={{5}^{5}}$

Vậy phương trình có 1 nghiệm.