Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.5 - Exponential and Logarithmic Equations - Exercise Set: 28

Answer

$x \approx 1.12$

Work Step by Step

Divide $4$ on both sides of the equation to obtain: $e^{7x}=\dfrac{10,273}{4}$ RECALL: $\ln{e^m}=m$ Take the natural logarithm of both sides to obtain: $\ln{e^{7x}}=\ln{(\frac{10,273}{4})}$ Use the rule above to obtain: $7x=\ln{(\frac{10,273}{4})}$ Divide both sides by $7$ to obtain: $x = \dfrac{\ln{(\frac{10,273}{4})}}{7}$ Use a scientific calculator to obtain: $x=1.121568573 \\x \approx 1.12$
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