Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Chapter Review - Review Exercises - Page 370: 24


$2 \log (x)+\dfrac{1}{2}\log(x^3+1)$

Work Step by Step

The given expression can be re-arranged as: $ \log(x^2 \sqrt {x^3+1}=\log[x^2 (x^3+1)^{1/2}]$ Use $\log_a{(mn)}=\log_a{m} + \log_a{n}$ to obtain: $\log[x^2 (x^3+1)^{1/2}]=\log (x^2) +\log (x^3+1)^{1/2}$ Use $\log_a{a^m}=m\log_a{m}$ to obtain: $ \log(x^2) +\log (x^3+1)^{1/2}=2 \log (x)+\dfrac{1}{2}\log(x^3+1)$
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