University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 1 - Section 1.6 - Inverse Functions and Logarithms - Exercises - Page 50: 59


$$t=4\ln^2 x$$

Work Step by Step

Another method to solve these exercises is to take the natural logarithm of both sides. In other words: $$e^x=a\hspace{1cm}\text{then}\hspace{1cm}\ln e^{x}=\ln a\hspace{1cm}\text{then}\hspace{1cm} x=\ln a$$ $$e^{\sqrt t}=x^2$$ - Take the natural logarithm of both sides: $$\ln(e^{\sqrt t})=\ln(x^2)$$ $$\sqrt t=\ln(x^2)$$ - Apply Power Rule: $$\sqrt t=2\ln x$$ $$t=(2\ln x)^2=4\ln^2 x$$
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