Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.4 Logarithmic Functions - 4.4 Assess Your Understanding - Page 322: 108


$\dfrac{\log_{10} {0.375}+7}{2}$

Work Step by Step

Divide $8$ to both sides of the equation to obtain: $10^{2x-7}=\dfrac{3}{8}$ $10^{2x-7}=0.375$ $\because a^y = x \text{ is equivalent to } \log_a x = y$ $\therefore 10^{2x-7}=0.37\implies \log_{10} 0.375=2x-7$ Solve the equation above to obtain: \begin{align*} 2x-7&=\log_{10} {0.375}\\\\ 2x&=\log_{10} {0.375}+7\\\\ x&=\dfrac{\log_{10} {0.375}+7}{2} \end{align*}
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