Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.9 Hyperbolic Functions - Exercises - Page 384: 2


$$\sinh \ln 5= \frac{12}{5}, \quad \tanh (3\ln 5) =\frac{7812}{7813}.$$

Work Step by Step

Using the fact that $x=e^{\ln x}$, we have $$\sinh \ln 5=\frac{e^{\ln 5}-e^{-\ln 5}}{2}=\frac{5-(1/5)}{2}=\frac{12}{5}$$ $$\tanh (3\ln 5)=\frac{e^{3\ln 5}-e^{-3\ln 5}}{e^{3\ln 5}+e^{-3\ln 5}}=\frac{5^3-5^{-3}}{5^3+5^{-3}}=\frac{7812}{7813}.$$
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