Answer
$\text{Exact: } \dfrac{\ln 1.2}{\ln 8}$
$\text{Approximately: } -0.088$
Work Step by Step
$\because a^y = b \text{ is equivalent to } y = \log_a b$
$\therefore 8^{-x}=1.2 \text{ is equivalent to } -x = \log_8 1.2$
Solve the equation above using the Change of Base Formula, which is $\hspace{20pt} \log_ a M = \dfrac{\log_b M}{\log_b a}$, to obtain:
$-x=\log_8 1.2 \\\\
-x= \dfrac{\ln 1.2}{\ln 8}\\\\
x= -\dfrac{\ln 1.2}{\ln 8}$
Therefore,
$ x = \boxed{-\dfrac{\ln 1.2}{\ln 8} \approx -0.088}$
