Answer
$x=-1$
Work Step by Step
RECALL:
$\log_a{x}=y \longrightarrow a^y=x, a\gt0, a\ne1$
Use the rule above to obtain:
$\log_2{(8^x)}=-3 \longrightarrow 2^{-3}=8^x$
Note that $8=2^3$. Write $8$ as $2^3$ to obtain:
$2^{-3} = (2^3)^x$
Use the rule $(a^m)^n=a^{mn}$ to obtain:
$2^{-3} = 2^{3x}$
Use the rule "$a^m=a^n\longrightarrow m=n$" to obtain:
$-3 = 3x$
Divide by 3 on both sides of the equation to obtain:
$\frac{-3}{3} = \frac{3x}{3}
\\-1=x$
