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: 17

Answer

$3$

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: $=\log_2{(\frac{6}{15})}+\log_2{20} \\=\log_2{(\frac{2}{5})}+\log_2{20}$ Use rule (1) above to obtain: $=\log_2{(\frac{2}{5}\cdot 20)} \\=\log_2{(\frac{40}{5})} \\=\log_2{8}$ Write $8$ as $2^3$ to obtain: $=\log_2{(2^3)}$ Use rule (3) above to obtain: $=3$
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