Answer
$\approx-0.088$
Work Step by Step
Take the $\log_8$ of both sides:
$\log_8{(8^{-x})}=\log_8{1.2}\\-x=\log_8{1.2}$
Multiply $-1$ to both sides to obtain
$x=-\log_8{1.2}$
We know that $\log_a {b}=\frac{\log_c {b}}{\log_c {a}}$ (Change of Base formula).
Hence, using the change-of-base formula and a calculator gives
$x=-\log_8{1.2}=-\frac{\ln{1.2}}{\ln{8}}=-0.08768\approx-0.088$
