Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 5 - Logarithmic Functions - Exercises to Skills for Chapter 5 - Page 232: 28

Answer

$\log(3x)$

Work Step by Step

Use the fact that $\log a^b=b\log a$ and $(a^b)^n=a^{bn}$ to simplify. $$2\log \sqrt{x}=2 \log x^{\frac{1}{2}}=\log {(x^\frac{1}{2}})^2=\log(x)$$ Finally, use the fact that $\log(ab)=\log(a)+\log(b)$ to simplify the expression to $$\log x + \log 3 = \log(3x)$$
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