Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises - Page 452: 3


(a) $e^{-ln2}=\frac{1}{2}$ (b) $e^{ln(lne^{3})}=3$

Work Step by Step

The exponential function is defined by if $e^{x}=y$ then $x =lny$. (a) $e^{-ln2}=\frac{1}{2}$ (b) Let $lnz=e^{ln(lne^{3})}$ $z=ln(e^{3}) = 3lne$ $=3$ Hence, $e^{ln(lne^{3})}=3$
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