Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 5 - Logarithmic Functions - Strengthen Your Understanding - Page 228: 23



Work Step by Step

First, divide both sides of the equation by $a$ to get $$b^t=\frac{n}{a}$$ Next, take the $\log$ of both sides to get $$\log b^t=\log(n/a)$$ Since $\log a^b=b \log a$ for all positive values of $a$, $$t \log b = log(n/a)$$ Finally, divide both sides by $\log b$ to get $$t = \frac{\log(n/a)}{\log b}$$ Thus, the statement is true.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.