Answer
$\dfrac{1}{2}$
Work Step by Step
$\because y=\log_a x \text{ is equivalent to } x= a^y$
$\therefore 3 = \log_x \left(\dfrac{1}{8} \right) \text{ is equivalent to } \dfrac{1}{8}=x^3$
Solve the equation to obtain:
$$x^3=\dfrac{1}{8}$$
$$x=\sqrt[3]{\dfrac{1}{8}} $$
$$x=\sqrt[3]{\left(\frac{1}{2}\right)^3}$$
$$x=\dfrac{1}{2}$$
