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: 50

Answer

$\log_2{\left(\frac{\sqrt{5}}{49}\right)}$

Work Step by Step

RECALL: (1) $\log_b{P} + \log_b{Q} = \log_b{(PQ)}$ (2) $\log_b{P} - \log_b{Q} = \log_b{(\frac{P}{Q})}$ (3) $a(\log_b{x}) = \log_b{(x^a)}$ Use rule (3) above to obtain: $=\log_2{(5^{\frac{1}{2}})}-\log_2{(7^2)} \\=\log_2{(5^{\frac{1}{2}})}-\log_2{49}$ Write $5^{\frac{1}{2}}$ as $\sqrt{5}$ to obtain: $=\log_2{\sqrt{5}}-\log_2{49}$ Use rule (2) above to obtain: $=\log_2{\left(\frac{\sqrt{5}}{49}\right)}$
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