Answer
$\frac{1}{2}$$\ln (x^4+2)$
Work Step by Step
$Expand$ $the$ $expression$:
$\ln \sqrt {x^4 + 2}$
Rewrite the square root
$\ln (x^4+2)^\frac{1}{2}$
Apply the Third Law of Logarithms
$\ln (x^4+2)^\frac{1}{2}$ = $\frac{1}{2}$$\ln (x^4+2)$
There are no Laws of Logarithms for adding/subtracting so we leave it as the answer
$\frac{1}{2}$$\ln (x^4+2)$