College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.4 - Logarithmic Functions - 6.4 Assess Your Understanding: 110

Answer

$x = \dfrac{\log{(\frac{3}{8})} + 7}{2} $

Work Step by Step

Divide both sides of the equation by 8 to obtain: $\dfrac{8 \cdot 10^{2x-7}}{8} = \dfrac{3}{8} \\10^{2x-7}=\dfrac{3}{8}$ Take the common logarithm of both sides to obtain: $\log{(10^{2x-7})}=\log{(\frac{3}{8})}$ Note that $\log{(10^x}) = x$. Thus, the equation above is equivalent to: $2x-7=\log{(\frac{3}{8})}$ Add $7$ to both sides of the equation to obtain: $2x-7+7 = \log{(\frac{3}{8})} + 7 \\2x = \log{(\frac{3}{8})} + 7$ Divide by 2 on both sides of the equation to obtain: $\dfrac{2x}{2} = \dfrac{\log{(\frac{3}{8})} + 7}{2} \\x = \dfrac{\log{(\frac{3}{8})} + 7}{2} $
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