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 49: 51


$$y=e^{5t}+b$$ on condition that $y\gt b$.

Work Step by Step

To solve natural logarithm equations, keep in mind this property: - If $\ln x = \ln a$ then $x=a$ $$\ln (y-b)=5t$$ - Condition: $y\gt b$ - Recall the property: $\ln e^x=x$ That means $5t=\ln e^{5t}$ Therefore, $$\ln(y-b) = \ln e^{5t}$$ $$y-b=e^{5t}$$ $$y=e^{5t}+b$$
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