Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 6 - Logarithmic Functions - Chapter Review Exercises: 53

Answer

$x \approx 3.98$

Work Step by Step

$\log (8x^{5}) - \log (2x) = 3$ $\log \frac{8x^{5}}{2x} = 3$ $\log \frac{8x^{4}}{2} = 3$ $\log 4x^{4} = 3$ $10^{3} = 4x^{4}$ $1000 = 4x^{4}$ $250 = x^{4}$ $x = 250^{\frac{1}{4}}$ $x$ must be greater than zero, so we take only the positive root. $x = 3.976...$ $x \approx 3.98$ Check: $\log (8x^{5}) - \log (2x) \overset{?}{=} 3$ $\log (8(3.976...)^{5}) - \log (2(3.976...)) \overset{?}{=} 3$ $\log (8(994.088...)) - \log (7.952) \overset{?}{=} 3$ $\log (7952.707...) - \log (7.952) \overset{?}{=} 3$ $3=3$
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