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 - 6.5 Solving Exponential Equations - 6.5 Exercises: 30

Answer

$x \approx 0.567$

Work Step by Step

$5(4)^{3x+2} - 830 = 14.5$ $5(4)^{3x+2} = 14.5 + 830$ $5(4)^{3x+2} = 844.5$ $(4)^{3x+2} = 168.9$ $3x + 2 = \log_4 168.9$ $3x = \log_4 168.9 - 2$ $x = \frac{(\log_4 168.9) - 2}{3}$ $x = \frac{(\frac{\log 168.9}{\log 4}) - 2}{3}$ by GDC / calculator $x = 0.566670...$ $x \approx 0.567$
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