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: 37



Work Step by Step

$2\log_{8}x-\dfrac{2}{3}\log_{8}x+4\log_{8}x$ Take the numbers multiplying in front of each $\log$ as exponents: $\log_{8}x^{2}-\log_{8}x^{2/3}+\log_{8}x^{4}=...$ Combine $\log_{8}x^{2}-\log_{8}x^{2/3}$ as the $\log$ of a division: $...=\log_{8}\dfrac{x^{2}}{x^{2/3}}+\log_{8}x^{4}=...$ Combine $\log_{8}\dfrac{x^{2}}{x^{2/3}}+\log_{8}x^{4}$ as the $\log$ of a product and simplify: $...=\log_{8}\dfrac{x^{2}\cdot x^{4}}{x^{2/3}}=\log_{8}\dfrac{x^{6}}{x^{2/3}}=\log_{8}x^{16/3}$
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