## Calculus 8th Edition

$4lns+\frac{1}{2}lnt+\frac{1}{4}lnu$
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 $ln(p)^{m}= m lnp$ $ln(s^{4}t^{\frac{1}{2}} u^{\frac{1}{4}})=ln(s^{4})+ln(t^{\frac{1}{2}})+ln (u^\frac{1}{4})$ Hence, $ln(s^{4})+ln(t^{\frac{1}{2}})+ln (u^\frac{1}{4})=4lns+\frac{1}{2}lnt+\frac{1}{4}lnu$