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 - Mid-Chapter Check Point: 32

Answer

$\log_7{\left(\frac{x^8}{\sqrt[3]{y}}\right)}$

Work Step by Step

RECALL: (1) $\log_b{m} - \log_b{n} = \log_b{(\frac{m}{n})}$ (2) $\log_b{m} + \log_b{n} = \log_b{(mn)}$ (3) $n \cdot \log_b{m} = \log_b{(m^n)}$ Use rule (3) above to obtain: $=\log_7{(x^8)} - \log_7{(y^{\frac{1}{3}})}$ Use rule (1) above to obtain: $=\log_7{\left(\frac{x^8}{y^{\frac{1}{3}}}\right)}$ Use the rule $a^{\frac{1}{3}} = \sqrt[3]{a}$ to obtain: $=\log_7{\left(\frac{x^8}{\sqrt[3]{y}}\right)}$
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