# How do you find the exact value of log_5(1/125)?

$- 3$
${\log}_{5} \left(\frac{1}{125}\right) = {\log}_{5} \left({125}^{-} 1\right)$
$= {\log}_{5} {\left({5}^{3}\right)}^{-} 1 = {\log}_{5} {5}^{-} 3 = - 3 {\log}_{5} 5 = - 3 \left(1\right) = - 3$