Answer
$x\approx -3.96$
Work Step by Step
RECALL:
$\log_b{x}=y \longrightarrow b^y=x$
Write the equation in exponential form using the rule above to obtain:
$3^{-3}=x+4
\\\frac{1}{3^3}=x+4
\\\frac{1}{27}=x+4$
Solve for $x$ to obtain:
$\begin{array}{ccc}
&\frac{1}{27}-4 &= &x+4-4
\\&\frac{1}{27} -3\frac{27}{27}&=&x
\\&-3\frac{26}{27} &= &x
\\&x &\approx &-3.96\end{array}$