Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.6 - Properties of Logarithms - Exercise Set: 36

Answer

$2\log_{5}x+\dfrac{1}{3}\log_{5}x-3\log_{5}(x+5)=\log_{5}\dfrac{x^{7/3}}{(x+5)^{3}}$

Work Step by Step

$2\log_{5}x+\dfrac{1}{3}\log_{5}x-3\log_{5}(x+5)$ Take the numbers multiplying in front of each $\log$ as exponents: $\log_{5}x^{2}+\log_{5}x^{1/3}-\log_{5}(x+5)^{3}=...$ Combine $\log_{5}x^{2}+\log_{5}x^{1/3}$ as the $\log$ of a product: $...=\log_{5}x^{2}\cdot x^{1/3}-\log_{5}(x+5)^{3}=...$ $...=\log_{5}x^{7/3}-\log_{5}(x+5)^{3}=...$ Combine $\log_{5}x^{7/3}-\log_{5}(x+5)^{3}$ as the $\log$ of a division: $...=\log_{5}\dfrac{x^{7/3}}{(x+5)^{3}}$ or $\log_{5}\dfrac{\sqrt[3]{x^{7}}}{(x+5)^{3}}$
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