Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 11 - 11.4 - Mathematical Induction - 11.4 Exercises - Page 806: 38


The property was verified for $n=1$. The property was verified when $n$ was changed by $n+1$.

Work Step by Step

Prove the property for $n=1$. $\ln x_1=\ln x_1$ The property is verified for $n=1$. Assuming that $\ln(x_1x_2...x_n)=\ln x_1+\ln x_2+...+\ln x_n$ for all integers $n\geq1$, we need to prove that $\ln(x_1x_2...x_nx_{n+1})=\ln x_1+\ln x_2+...+\ln x_n+\ln x_{n+1}$: $\ln(x_1x_2...x_nx_{n+1})=\ln(x_1x_2...x_n)+\ln x_{n+1}=\ln x_1+\ln x_2+...+\ln x_n+\ln x_{n+1}$
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.