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: 10

Answer

$\log{x}-3$

Work Step by Step

RECALL: The quotient rule for logarithms states: $\log{\left(\frac{b}{c}\right)} = \log{b} - \log{c}$ Use the quotient rule to obtain: $\log{\left(\frac{x}{1000}\right)} \\= \log{x} - \log{1000} \\=\log{x} - \log{(10^3})$ Note that for all real numbers within its domain, $\log{(10^n)}=n$. This means that $\log{(10^3)} =3$. Thus, $\log{x} -\log{(10^3)}= \log{x}-3$
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