Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.3 Logarithmic Functions - 6.3 Exercises - Page 426: 14


$log_{10}\frac{4a}{\sqrt[3] (a+1)}$

Work Step by Step

Use logarithmic properties $ln(pq) = lnp+lnq$, $ln(\frac{p}{q}) = lnp-lnq$ and $ln(p)^{m}= m lnp$. $log_{10}4+log_{10}a-\frac{1}{3}log_{10}(a+1)=log_{10}(4a)-log_{10}(a+1)^{\frac{1}{3}}$ This implies $log_{10}4+log_{10}a-\frac{1}{3}log_{10}(a+1)=log_{10}\frac{4a}{\sqrt[3] (a+1)}$
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