#### Answer

$\log(y^4\sqrt{x})$

#### Work Step by Step

Use the fact that $\log a^b=b\log a$ to simplify. $$\frac{1}{2}\log x=\log x^{\frac{1}{2}}=\log \sqrt{x}$$ $$4 \log y = \log y^4$$ Finally, use the fact that $\log(ab)=\log(a)+\log(b)$ to simplify the expression to $$\log \sqrt{x}+\log y^4=\log(y^4\sqrt{x})$$