Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.3 - Properties of Logarithms - Exercise Set: 5

Answer

$3 + \log{x}$

Work Step by Step

RECALL: (i) $\log_b{MN}=\log_b{M} + \log_b{N}$ (Product Rule). (ii) $\log{x}=\log_{10}{x}.$ (iii) $\log_b{b^x}=x.$ Use the product rule with $M=1000$ and $N=x$ to obtain $\log{1000} + \log{x} \\=\log{10^3} + \log{x}.$ Use rule (ii) above to obtain $\log_{10}{10^3}+\log_{10}{x}.$ Use rule (iii) above with $b=10$ to obtain $3 + \log_{10}{x}.$ Use rule (ii) above to obtain $3 + \log{x}.$
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