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: 34

Answer

$\frac{2}{3}$

Work Step by Step

Since $25=5^2$, the given expression is equivalent to: $=\log_5{(\sqrt[3]{5^2})}$ RECALL: $\sqrt[n]{a^m} = a^{\frac{m}{n}}, a \ge 0$ Use the rule above to obtain: $\log_{5}{(\sqrt[3]{5^2})}=\log_{5}{(5^{\frac{2}{3}})}$ RECALL: $\log_a{(a^n)} = n, a \gt0, a\ne1$ Using the rule above gives: $\log_{5}{(5^{\frac{2}{3}})}=\frac{2}{3}$ Thus, $\log_{5}{\sqrt[3]{25}}=\frac{2}{3}$
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