Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Review: 88

Answer

{$\frac{1}{4}(\frac{\log 3}{\log 8}+2)$}, {$0.6321$}

Work Step by Step

Step 1: $8^{4x-2}=3$ Step 2: $\log 8^{4x-2}=\log 3$ Step 3: $(4x-2)\log 8=\log 3$ Step 4: $(4x-2)=\frac{\log 3}{\log 8}$ Step 5: $4x=\frac{\log 3}{\log 8}+2$ Step 6: $x=\frac{1}{4}(\frac{\log 3}{\log 8}+2)\approx0.6321$ Therefore, the exact solution is {$\frac{1}{4}(\frac{\log 3}{\log 8}+2)$} whereas the four decimal approximation is {$0.6321$}.
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