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 - Section 9.4 - Properties of Logarithms - Exercise Set: 11

Answer

$3 - \log_4{y}$

Work Step by Step

RECALL: The quotient rule for logarithms states: $\log_a{\left(\frac{b}{c}\right)} = \log_a{b} - \log_a{c}$ Use the quotient rule to obtain: $\log_4{\left(\frac{64}{y}\right)} \\= \log_4{64} - \log_4{y} \\=\log_4{(4^3)} - \log_4{y}$ Note that for all real numbers within its domain, $\log_a{(a^n)}=n$. This means that $\log_4{(4^3)} =3$. Thus, $\log_4{(4^3)} - \log_4{y}= 3 - \log_4{y}$
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