Answer
$4lns+\frac{1}{2}lnt+\frac{1}{4}lnu$
Work Step by Step
Consider the quantity $ln[(s^{4}\sqrt (t\sqrt u)]$as follows:
$ln[(s^{4}\sqrt (t\sqrt u)$=$ln[(s^{4} (t\sqrt u)^{\frac{1}{2}}]$
This implies
$ln[(s^{4}\sqrt (t\sqrt u)$=$ln(s^{4}t^{\frac{1}{2}} u^{\frac{1}{4}})$
Use logarithmic properties $ln(pq) = lnp+lnq$ and $ln(p)^{m}= m lnp$
$ln(s^{4}t^{\frac{1}{2}} u^{\frac{1}{4}})=ln(s^{4})+ln(t^{\frac{1}{2}})+ln (u^\frac{1}{4})$
$ln(s^{4})+ln(t^{\frac{1}{2}})+ln (u^\frac{1}{4})=4lns+\frac{1}{2}lnt+\frac{1}{4}lnu$