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: 33

Answer

$log_{10}(x^{2}+8x+15)$

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, $log_{10}(x+3)+log_{10}(x+5)=log_{10}((x+3)(x+5))$. We can use the FOIL method to further simplify. $log_{10}((x+3)(x+5))=log_{10}(x^{2}+5x+3x+15)=log_{10}(x^{2}+8x+15)$.
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