Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.4 - Exponential and Logarithmic Equations - Exercise Set: 32

Answer

$x \approx 1.12$

Work Step by Step

Divide both sides of the equation by 4 to obtain $e^{7x}=\dfrac{10,273}{4}.$ The base in the exponential equation is $e$, so take the natural logarithm on both sides to obtain $\ln{e^{7x}}=\ln{\frac{10273}{4}}.$ Use the property $\ln{e^b}=b$ (where b=7x) on the left side to obtain $7x = \ln{\frac{10273}{4}}.$ Divide both sides by $7$ to obtain $x=\dfrac{\ln{\frac{10273}{4}}}{7}.$ Use a calculator and round-off the answer to two decimal places to obtain $x \approx 1.12.$
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