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: 12

Answer

$3-\log_5{y}$

Work Step by Step

RECALL: The quotient rule for logarithms states: $\log_a(\frac{b}{c})=\log_a{b}−\log_a{c}$ Use the quotient rule to obtain: $=\log_5(125)-\log_5{y} \\=\log_5{(5^3)}-\log_5{y}$ Note that for all real numbers within its domain, $\log_a{(a^n)}=n$. This means that $\log_5{(5^3)}=3$. Thus, $\log_5{(5^3)}-\log_5{y}=3-\log_5{y}$
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