Answer
$\dfrac{1}{3}$
Work Step by Step
The domain of the variable requires that $x>0$.
Recall:
$\log_a M^r = r \log_a M$
This means that:
$3\log_2 x = \log_2 x^3\\\\
- \log_2 27 = \log_2 27^{-1}$
Thus, the given equation is equivalent to:
$\log_2 x^3 = \log_2 27^{-1}$
Recall also that:
$\text{If } \log_a M = \log_a N \text{, then } M=N$
Therefore
$x^3 = 27^{-1}$
$x^3 = \dfrac{1}{27}$
$x= \sqrt[3]{\dfrac{1}{27}}$
$x = \boxed{\dfrac{1}{3}}$
