[tex]3^x\cdot3^{-1}+3^x+3^x\cdot3^1=\frac{13}{27}\\\\\frac{3^x}{3^1}+3^x+3\cdot3^x=\frac{13}{27}[/tex]
Consideremos [tex]3^x=k[/tex], segue,
[tex]\frac{k}{3}+k+3k=\frac{13}{27}\\\\\frac{k}{3/9}+\frac{4k}{1/27}=\frac{13}{27/1}\\\\9k+108k=13\\\\117k=13\\\\k=\frac{13}{117}\\\\k=\frac{1}{9}[/tex]
Portanto,
[tex]3^x=k\\\\3^x=\frac{1}{9}\\\\3^x=\frac{1}{3^2}\\\\3^x=3^{-2}\\\\x=-2\\\\x^{-1}=(-2)^{-1}\\\\\boxed{\boxed{x^{-1}=-\frac{1}{2}}}[/tex]
