Chapter 3 - Section 3.4 - Exponential and Logarithmic Equations - Exercise Set - Page 489: 57

$x\approx -3.96$

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: $\begin{array}{ccc} &\frac{1}{27}-4 &= &x+4-4 \\&\frac{1}{27} -3\frac{27}{27}&=&x \\&-3\frac{26}{27} &= &x \\&x &\approx &-3.96\end{array}$