Answer
$x=\dfrac{1}{2}$
Work Step by Step
RECALL:
$\log_a{x} = y \longrightarrow a^y=x, a\gt0, a\ne 1$
Use the definition above to obtain:
$\log_x{(\frac{1}{8})}=3
\\
\longrightarrow x^3=\frac{1}{8}
\\x^3 = \frac{1}{2^3}
\\x^3=(\frac{1}{2})^3$
Take the cube root of both sides to obtain:
$x = \sqrt[3]{(\frac{1}{2})^3}$
Use the rule $\sqrt[3]{a^3} = a$ to obtain:
$x = \frac{1}{2}$
