Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.4 - Laws of Logarithms - 4.4 exercises: 50

Answer

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

Work Step by Step

$Combine$ $the$ $expression$: $\frac{1}{2}$$\log_2 5$ - $2$$\log_2 7$ Apply the Third Law of Logarithms for $\frac{1}{2}$$\log_2 5$ and $2$$\log_2 7$ $\frac{1}{2}$$\log_2 5$ = $\log_2 5^\frac{1}{2}$ $2$$\log_2 7$ = $\log_2 7^2$ $\log_2 5^\frac{1}{2}$ - $\log_2 7^2$ $\log_2 \sqrt{5}$ - $\log_2 7^2$ [Note: 5$^\frac{1}{2}$ = $\sqrt{5}$] Apply the Second Law of Logarithms $\log_2 \sqrt{5}$ - $\log_2 7^2$ = $\log_2 (\frac{\sqrt{5}}{7^2})$ $\log_2 (\frac{\sqrt{5}}{49})$
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