College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.4 - Laws of Logarithms - 4.4 Exercises: 18

Answer

$-2$

Work Step by Step

RECALL: (1) $\log_b{M}+\log_b{N}=\log_b{MN}$ (2) $\log_b{M}−\log_b{N}=\log_b{\frac{M}{N}}$ (3) $\log_b{(b^x)}=x$ (4) $\log_b{b}=1$ Use rule (2) above to obtain: $=\log_3{(\frac{100}{18})}-\log_3{50} \\=\log_3{(\frac{50}{9})}-\log_3{50}$ Use rule (2) above to obtain: $=\log_3{\left(\dfrac{\frac{50}{9}}{50}\right)} \\=\log_3{\left(\frac{50}{9(50)}\right)}$ Cancel the common factor $50$ to obtain: $=\log_3{(\frac{1}{9})}$ Write $9$ as $3^2$ to obtain: $=\log_3{(\frac{1}{3^2})}$ Use the rule $\dfrac{1}{a^m} = a^{-m}$ to obtain: $=\log_3{(3^{-2})}$ Use rule (3) above to obtain: $=-2$
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