Answer
$log_{3}\frac{1}{6}\approx-1.6309$
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, $log_{3}\frac{1}{6}=\frac{log_{10}\frac{1}{6}}{log_{10}3}=\frac{-.7782}{.4771}\approx-1.6309$.
