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: 10

Answer

$\log{x} - 3$

Work Step by Step

RECALL: (i) $\log_b{\frac{M}{N}}=\log_b{M} - \log_b{N}$ (Quotient Rule). (ii) $\log{x}=\log_{10}{x}.$ (iii) $\log_b{b^x}=x.$ Use the quotient rule with $M=x$ and $N=1000$ to obtain $\log{x} - \log{1000} \\=\log{x} - \log{10^3}.$ Simplify the second term by using rules (ii) and (iii) above to obtain $\log{x} -\log_{10}{10^3} \\=\log{x} - 3.$
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