Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 6 - Logarithmic Functions - Chapter Review Exercises: 23

Answer

$= \frac{1}{5}\log_7 3 + \frac{3}{5}\log_7 x + \frac{1}{5}\log_7 y$

Work Step by Step

$\log_7 (\sqrt[5] {3x^{3}y})$ $= \log_7 (3x^{3}y)^{\frac{1}{5}}$ $= \log_7 (3^{\frac{1}{5}}x^{3 \times \frac{1}{5} }y^{\frac{1}{5}})$ $= \log_7 (3^{\frac{1}{5}}x^{\frac{3}{5} }y^{\frac{1}{5}})$ $= \log_7 (3^{\frac{1}{5}}) + \log_7 x^{\frac{3}{5}} + \log_7 y^{\frac{1}{5}}$ $= \frac{1}{5}\log_7 3 + \frac{3}{5}\log_7 x + \frac{1}{5}\log_7 y$
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