Answer
$-3$
Work Step by Step
Note that $27=3^3$.
Thus,
$\log_3{(\frac{1}{27})}=\log_3{(\frac{1}{3^3})}$
Use the rule $\dfrac{1}{a^m} = a^{-m}$ to obtain:
$\log_3{(\frac{1}{3^3})} = \log_3{(3^{-3})}$
RECALL:
$\log_a{(a^n)} = n$
Use the rule above to obtain:
$\log_3{(3^{-3})} = -3$
