\(7\times3^{x-1}-3^{x+2}=-540\)
\(7\times3^{x-1}-3^{x-1}\times3^3=-540\)
\(3^{x-1}\left(7-3^3\right)=-540\)
\(3^{x-1}\left(7-27\right)=-540\)
\(3^{x-1}\times\left(-20\right)=-540\)
\(3^{x-1}=\left(-540\right)\div\left(-20\right)\)
\(3^{x-1}=27\)
\(3^{x-1}=3^3\)
\(\Rightarrow x-1=3\)
\(x=4\)
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