[tex]\displaystyle\\
\left(\frac{1}{3}\right)^x = \sqrt{27} \\\\\\
\frac{1}{3^x} = 27^{ \frac{1}{2}}\\\\\\
3^{-x} = \Big(3^3\Big)^{ \frac{1}{2}}\\\\\\
3^{-x} = 3^{3\cdot\frac{1}{2}}\\\\
-x = 3\cdot\frac{1}{2}\\\\\\
-x = \frac{3}{2}~~~\Big| ~ \cdot(-1)\\\\\\
\boxed{x = -\frac{3}{2}}
[/tex]