#### Answer

-0.6309

#### Work Step by Step

From the change of base formula, we know that $log_{b}a=\frac{log_{c}a}{log_{c}b}$ ($a$, $b$, and $c$ are positive real numbers and neither $b$ nor $c$ is equal to 1).
Therefore, $log_{\frac{1}{3}}2=\frac{log_{10}2}{log_{10}\frac{1}{3}}=\frac{0.3010}{-0.4771}=-0.6309$.