\(\left(3x-6\right)^{5021}=\left(3x-6\right)^{5020}\\ \Leftrightarrow\left(3x-6\right)^{5020}.\left(3x-6\right)=\left(3x-6\right)^{5020}\\ \Leftrightarrow3x-6=0\\ \Leftrightarrow x=2\)
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\(\left(3x-6\right)^{5021}=\left(3x-6\right)^{5020}\)
\(\left(3x-6\right)^{5021}-\left(3x-6\right)^{5020}=0\)
\(\left(3x-6\right)^{5020}\left(3x-6-1\right)=0\)
\(\left(3x-6\right)^{5020}\left(3x-7\right)=0\)
⇔ \(\left[{}\begin{matrix}3x-6=0\\3x-7=0\end{matrix}\right.\)
⇔ \(\left[{}\begin{matrix}3x=6\\3x=7\end{matrix}\right.\)
⇔ \(\left[{}\begin{matrix}x=2\\x=\dfrac{7}{3}\end{matrix}\right.\)
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