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 - 6.6 Solving Logarithmic Equations - 6.6 Exercises - Page 535: 62

Answer

$x \approx 0.315$

Work Step by Step

$5 \log (2x) + 4 = 3$ $5\log 2x = 3 - 4$ $5 \log 2x = -1$ $\log 2x = -\frac{1}{5}$ $10^{(-\frac{1}{5})} = 2x$ $x = \frac{10^{(-\frac{1}{5})}}{2}$ $x \approx 0.315$ Check: $5 \log (2x) + 4 \overset{?}{=} 3$ $5 \log (2(\frac{10^{(-\frac{1}{5})}}{2})) + 4 \overset{?}{=} 3$ $5 \log (10^{(-\frac{1}{5})}) + 4 \overset{?}{=} 3$ $5(-0.2) + 4 \overset{?}{=} 3$ $-1 + 4 \overset{?}{=} 3$ $3 = 3$
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