Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Review - Exercises - Page 389: 46


$\log_2 x + \frac{1}{2}\log_2 (x^2+1)$

Work Step by Step

$Expand$ $the$ $logarithmic$ $expression:$ $\log_2 (x\sqrt {x^2+1})$ Use the First Law of Logarithms $$\log_2 (x\times \sqrt {x^2+1}) = \log_2 x + \log_2 \sqrt {x^2+1}$$ Rewrite the root to exponent form $$\log_2 x + \log_2 (x^2+1)^{\frac{1}{2}}$$ Use the Third Law of Logarithms for $\log_2 (x^2+1)^{\frac{1}{2}}$ $$\log_2 (x^2+1)^{\frac{1}{2}} = \frac{1}{2}\log_2 (x^2+1)$$ $$\log_2 x + \frac{1}{2}\log_2 (x^2+1)$$
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