[tex]3^{x-1}+3^{x+1}=\frac{13}{27} \\
\\
\frac{3^x}{3}}+3^x.3=\frac{13}{27} \\
\\
9.3^x+81.3^x=13 \\
\\
fazendo \ y=3^x \\
\\
9y+81y=13 \\
\\
90y=13 \\
\\
y=\frac{13}{90} \\
\\
3^x=\frac{13}{90} \\
[/tex]
[tex]3^x=\frac{13}{90} \\
log3^x=log13-log90 \\
xlog3=log13-log90 \\
\\
x=\frac{log13-log90}{log3} \\
\\
\boxed{x=-1,7611}[/tex]
-2 < x < -1
