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: 5

Answer

$3 + \log{x}$

Work Step by Step

RECALL: The product rule for logarithms: $\log_a{bc} = \log_a{b} + \log_a{c}$ Use the product rule to obtain: $\log{(1000x)} \\= \log{(1000 \cdot x)} \\= \log{1000} + \log{x} \\=\log{10^3} + \log{x}$ Note that for all real numbers within its domain $\log{10^n}=n$. This means that $\log{10^3} =3$. Thus, $\log{10^3} + \log{x}= 3 + \log{x}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.