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: 29

Answer

10$\log_2 x$ + 10$\log_2 y$

Work Step by Step

$Expand$ $the$ $expression$: $\log_2 (xy)^{10}$ Distribute the exponent to the variables in the parenthesis $\log_2 (x^{10}y^{10})$ Apply the First Law of Logarithms $\log_2 (x^{10}\times y^{10})$ = $\log_2 x^{10}$ + $\log_2 y^{10}$ Apply the Third Law of Logarithms to both terms $\log_2 x^{10}$ + $\log_2 y^{10}$ = 10$\log_2 x$ + 10$\log_2 y$
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