Answer
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 $\ln(x_1x_2...x_nx_{n+1})=\ln x_1+\ln x_2+...+\ln x_n+\ln x_{n+1}$:
$\ln(x_1x_2...x_nx_{n+1})=\ln(x_1x_2...x_n)+\ln x_{n+1}=\ln x_1+\ln x_2+...+\ln x_n+\ln x_{n+1}$
