Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 9 - Section 9.4 - Properties of Logarithms - 9.4 Exercises: 34

Answer

$log_{10}(x^{2}+10x+24)$

Work Step by Step

We know that $log_{b}xy=log_{b}x+log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$). Therefore, $log_{10}(x+4)+log_{10}(x+6)=log_{10}((x+4)(x+6))$. We can use the FOIL method to further simplify. $log_{10}((x+4)(x+6))=log_{10}(x^{2}+6x+4x+24)=log_{10}(x^{2}+10x+24)$.
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