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: 32

Answer

$\log_3 x$ + $\frac{1}{2}$$\log_3 y$

Work Step by Step

$Expand$ $the$ $expression$: $\log_3 (x \sqrt{y})$ Rewrite the root for y $\log_3 (xy^\frac{1}{2})$ Apply the First Law of Logarithms $\log_3 (x\times y^\frac{1}{2})$ = $\log_3 x$ + $\log_3 y^\frac{1}{2}$ Apply the Third Law of Logarithms for $\log_3 y^\frac{1}{2}$ $\log_3 y^\frac{1}{2}$ = $\frac{1}{2}$$\log_3 y$ $\log_3 x$ + $\log_3 y^\frac{1}{2}$ = $\log_3 x$ + $\frac{1}{2}$$\log_3 y$
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