Answer
$x=\dfrac{1}{3}$
Work Step by Step
Recall:
(1) $n\log_a{x}=\log_a{x^n}$
(2) $\log_a{x}=\log_a{y}\longrightarrow x=y$
(3) $a^m=b^m\longrightarrow a=b$
The gievn equation is equivalent to:
$$3\log_2{x}=-1\cdot \log_2{27}$$
Thus, using rule (1) above gives:
$$\log_2{x^3}=\log_2{27^{-1}}$$
Using rule (2) above gives:
\begin{align*}
x^3&=27^{-1}\\
x^3&=\frac{1}{27^1}\\
x^3&=\frac{1}{27}\\
x^3&=\left(\frac{1}{3}\right)^3
\end{align*}
Use rule (3) above to obtain:
$$x=\dfrac{1}{3}$$
