Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.4 - Properties of Logarithms - Exercise Set: 30

Answer

$\frac{1}{2} + \frac{1}{2}\ln{x}$

Work Step by Step

Note that $\sqrt{ex} = (ex)^{\frac{1}{2}}$ therefore the expression above is equivalent to: $=\ln{(ex)^{\frac{1}{2}}}$ RECALL: (1) $\ln{(b^c)}=c \cdot \ln{b}$ (2) $\ln{(xy)} = \ln{x} + \ln{y}$ (3) $\ln{(\frac{x}{y})}=\ln{x} - \ln{y}$ Use rule (1) above to obtain: $=\frac{1}{2}\ln{(ex)}$ Use rule (2) above to obtain: $=\frac{1}{2}(\ln{e} + \ln{x}) \\=\frac{1}{2}\ln{e} + \frac{1}{2}\ln{x}$ Use the rule $\ln{e} = 1$ to obtain: $=\frac{1}{2} \cdot 1 + \frac{1}{2}\ln{x} \\=\frac{1}{2} + \frac{1}{2}\ln{x}$
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