# How do you evaluate log_(1/13) (1/169)?

$2$
Spotting that $169 = {13}^{2}$ so you need ${\log}_{\frac{1}{13}} \left(\frac{1}{13} ^ 2\right)$.
Since ${\log}_{a} \left({x}^{2}\right) = 2 {\log}_{a} \left(x\right)$ and ${\log}_{a} \left(a\right) = 1$ you get
${\log}_{\frac{1}{13}} \left({\left(\frac{1}{13}\right)}^{2}\right) = 2 {\log}_{\frac{1}{13}} \left(\frac{1}{13}\right) = 2 \times 1 = 2$.