Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.4 - Laws of Logarithms - 4.4 exercises - Page 359: 30


$\frac{1}{2}$$\ln a$ + $\frac{1}{2}$$\ln b$

Work Step by Step

$Expand$ $the$ $expression$: $\ln \sqrt{ab}$ Rewrite the root to exponential form $\ln (ab)^{\frac{1}{2}}$ Apply the Third Law of Logarithms $\ln (ab)^{\frac{1}{2}}$ = $\frac{1}{2}$$\ln ab$ Apply the First Law of Logarithms and distribute the half to both terms $\frac{1}{2}$$\ln (a \times b)$ = $\frac{1}{2}$$\ln a$ + $\frac{1}{2}$$\ln b$
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