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: 16


$$y=\frac{\ln(\ln x)+\ln3}{\ln3}$$

Work Step by Step

$$3^y=3\ln x$$ Take the natural logarithm of both sides: $$\ln(3^y)=\ln(3\ln x)$$ Remember that $\ln x^a=a\ln x$ and $\ln(xy)=\ln x+\ln y$ $$y\ln3=\ln3+\ln(\ln x)$$ $$y=\frac{\ln(\ln x)+\ln3}{\ln3}$$
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