Answer
$log_{\frac{1}{3}}2\approx-.6309$
Work Step by Step
In order to evaluate the given logarithm, we can use the change of base formula.
$log_{b}a=\frac{log_{c}a}{log_{c}b}$ (where a, b, and c are positive real numbers and neither b nor c is 1)
For simplicity, we will use base 10, which is the base of the common logarithm.
Therefore, $log_{\frac{1}{3}}2=\frac{log_{10}2}{log_{10}\frac{1}{3}}=\frac{.3010}{-.4771}\approx-.6309$.
