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 - Page 712: 6


$4 + \log{x}$

Work Step by Step

RECALL: The product rule for logarithms: $\log{bc} = \log{b} + \log{c}$ Use the product rule to obtain: $\log{(10,000x)} \\= \log{(10,000 \cdot x)} \\= \log{10,000} + \log{x} \\=\log{10^4} + \log{x}$ Note that for all real numbers within its domain $\log{10^n}=n$. This means that $\log{10^4} =4$. Thus, $\log{10^4} + \log{x}= 4 + \log{x}$
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