College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.4 - Logarithmic Functions - 6.4 Assess Your Understanding - Page 449: 37

Answer

$\dfrac{1}{2}$

Work Step by Step

Since $\sqrt{e} = e^{\frac{1}{2}}$, then the given expression is equivalent to: $$\ln{e^{\frac{1}{2}}}$$ Let $\ln{e^{\frac{1}{2}}}=y$ Recall: $$\ln{x} = y \longrightarrow e^y=x$$ Use the rule above to obtain: $$\ln{e^{\frac{1}{2}}}=y \longrightarrow e^y=e^{\frac{1}{2}}$$ Using the rule $a^m=a^n\longrightarrow m=n$ gives: $$y=\dfrac{1}{2}$$
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