Answer
$-1$
Work Step by Step
$\because y=\log_a x \text{ is equivalent to } x= a^y$
$\therefore -3 = \log_2 8^x \text{ is equivalent to } 8^x=2^{-3}$
With $8=2^3$, use the rule $\left(a^m\right)^n=a^{mn}$ to obtain:
\begin{align*}
8^x&=2^{-3}\\\\
\left(2^3\right)^x&=2^{-3}\\\\
2^{3x}&=2^{-3}
\end{align*}
Solve the equation above using the rule $a^m=a^n \implies m=n$ to obtain:
\begin{align*}
3x&=-3\\\\
\frac{3x}{3}&=\frac{-3}{3}\\\\
x&=-1
\end{align*}
