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: 33

Answer

$\frac{1}{2}$

Work Step by Step

RECALL: $\sqrt{a} = a^{\frac{1}{2}}, a \ge 0$ Use the rule above to obtain: $\log_{10}{\sqrt{10}}=\log_{10}{(10^{\frac{1}{2}})}$ RECALL: $\log_a{(a^n)} = n, a \gt0, a\ne1$ Using the rule above gives: $\log_{10}{(10^{\frac{1}{2}})}=\frac{1}{2}$ Thus, $\log_{10}{\sqrt{10}}=\frac{1}{2}$
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