$(2x-1)^{1357}=(2x-1)^{1354}$
$\Leftrightarrow (2x-1)^{1357}-(2x-1)^{1354}=0$
$\Leftrightarrow (2x-1)^{1354}[(2x-1)^{3}-1]=0$
$\Leftrightarrow \left[ \begin{array}{l}(2x-1)^{1357}=0\\(2x-1)^{3}-1=0\end{array} \right.$
$\Leftrightarrow \left[ \begin{array}{l}2x-1=0\\2x-1=1\end{array} \right.$
$\Leftrightarrow \left[ \begin{array}{l}x=\frac{1}{2}\\x=1\end{array} \right.$
