College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 404: 37


(a) $x=-\ln 11.5$ (b) $x\approx -2.442347$

Work Step by Step

(a) We need to solve: $\frac{50}{1+e^{-x}}=4$ $50=4(1+e^{-x})$ $50=4+4e^{-x}$ $46=4e^{-x}$ $\frac{46}{4}=11.5=e^{-x}$ We take the log of both sides and use log rules to simplify: $\ln 11.5=\ln e^{-x}$ $\ln 11.5=-x$ $x=-\ln 11.5$ (b) We solve using a calculator: $x\approx -2.442347$
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