\(7.3^x+20.3^x=3^{25}\Rightarrow3^x\left(7+20\right)=3^{25}\)
\(\Rightarrow3^x.3^3=3^{25}\Rightarrow3^x=3^{22}\Rightarrow x=22\)
\(7\cdot3^x+20\cdot3^x=3^{25}\)
\(3^x\cdot\left(20+7\right)=3^{25}\)
\(3^x\cdot27=3^{25}\)
\(3^x\cdot3^3=3^{25}\)
\(3^x=3^{25}:3^3\)
\(3^x=3^{22}\)
\(x=22\)