Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Practice Exercises - Page 440: 82

Answer

$$ y = \frac{{\ln 3 + \ln (\ln x)}}{{\ln 3}} $$

Work Step by Step

$$\eqalign{ & {3^y} = 3\ln x \cr & {\text{take the natural logarithm on both sides}} \cr & \ln {3^y} = \ln \left( {3\ln x} \right) \cr & {\text{use power property for logarithms}} \cr & y\ln 3 = \ln \left( {3\ln x} \right) \cr & {\text{solve for }}y \cr & y = \frac{{\ln \left( {3\ln x} \right)}}{{\ln 3}} \cr & y = \frac{{\ln 3 + \ln (\ln x)}}{{\ln 3}}} $$
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