Answer
$k\approx-0.884$
Work Step by Step
$12^{-k}=9 \qquad \color{blue}{\text{ ...apply ln(...) to both sides } }$
$\ln 12^{-k}=\ln 9 \qquad \color{blue}{\text{ ...apply } \log_{a}x^{r}=r\log_{a}x}$
$-k\ln 12=\ln 9 \qquad \color{blue}{\text{ ... } /\div(-\ln 12)}$
$k=-\displaystyle \frac{\ln 9}{\ln 12}$
$k\approx-0.884$