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: 35

Answer

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

Work Step by Step

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

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.