Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.2* The Natural Logarithmic Functions - 6.2* Exercises: 4

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