Answer
$x=4\frac{1}{27}$
Work Step by Step
RECALL:
$\log_b{x}= y \longrightarrow b^y=x$
Use the rule above to obtain:
$3^{-3}=x-4
\\\dfrac{1}{3^3}=x-4
\\\dfrac{1}{27}=x-4$
Add $4$ on both sides of the equation to obtain:
$4+\dfrac{1}{27}=x
\\4\frac{1}{27}=x$