\(\left(3x-7\right)^{2018}=\left(3x-7\right)^{2016}\)
\(\Leftrightarrow\left(3x-7\right)^{2018}-\left(3x-7\right)^{2016}=0\)
\(\Leftrightarrow\left(3x-7\right)^{2016}\left[\left(3x-7\right)^2-1\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(3x-7\right)^{2016}=0\\\left(3x-7\right)^2-1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left(3x-7\right)^{2016}=0\\\left(3x-7\right)^2=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-7=0\\3x-7=1\\3x-7=-1\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}3x=7\\3x=8\\3x=6\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{3}\\x=\dfrac{8}{3}\\x=2\end{matrix}\right.\)
