University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 7 - Practice Exercises - Page 420: 17



Work Step by Step

$$\ln(y-1)=x+\ln y$$ We can rewrite $x=\ln e^x$ $$\ln(y-1)=\ln e^x+\ln y$$ Also, $\ln x+\ln y=\ln(xy)$ $$\ln(y-1)=\ln(e^xy)$$ We can take out the natural logarithm on both sides. $$y-1=e^xy$$ $$y-e^xy=1$$ $$y(1-e^x)=1$$ $$y=\frac{1}{1-e^x}$$
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