Use the law of logarithms to expand an expression $$\log\sqrt [ 3 ]{ \frac { x+2 }{ x^{ 4 }(x^{ 2 }+4) }  } $$
How is this answer incorrect?
$$\frac { 1 }{ 3 } [\log(x+2)-(4\log x+\log(x^ 2+4))]$$

Your answer is correct, with reservation about function domain. $Dom(log\sqrt[3]{\frac{x+2}{x^{4}(x^{2}+4)}})=\left(-2,\infty\right)/\{0\}$ 
$$ Dom[\frac{1}{3}(log(x+2)-(4log(x)+log(x^{2}+4)]=(0,\infty)$$
For example, if $x=-1$, original function give $-log(5)/3$, but your formula "Error"
