\(9^x.3^7=3^{x-1}\)
\(\Leftrightarrow\left(3^2\right)^x.3^7=3^{x-1}\)
\(\Leftrightarrow3^{2x}.3^7=3^{x-1}\)
\(\Leftrightarrow3^{2x+7}=3^{x-1}\)
\(\Leftrightarrow2x+7=x-1\)
\(\Leftrightarrow x-1-2x=7\)
\(\Leftrightarrow-x-1=7\)
\(\Leftrightarrow-x=8\)
\(\Leftrightarrow x=-8\)