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: 4

Answer

$ 1 + \log_9{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: $\log_9{(9x)} \\= \log_9{(9 \cdot x)} \\= \log_9{9} + \log_9{x}$ Note that for all real numbers within its domain, $\log_a{a}=1$. This means that $\log_9{9} = 1$. Thus, $\log_9{9} + \log_9{x}= 1 + \log_9{x}$
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