## Algebra and Trigonometry 10th Edition

The property was verified for $n=1$. The property was verified when $n$ was changed by $n+1$.
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 $\ln(x_1x_2...x_nx_{n+1})=\ln x_1+\ln x_2+...+\ln x_n+\ln x_{n+1}$: $\ln(x_1x_2...x_nx_{n+1})=\ln(x_1x_2...x_n)+\ln x_{n+1}=\ln x_1+\ln x_2+...+\ln x_n+\ln x_{n+1}$