Question 70
Given a geometric sequence $\left(a_{n}\right)$ with positive terms. Let's mark it
$$
S_{n}=\log a_{1}+\log a_{2}+\ldots+\log a_{n-1}+\log a_{n}
$$
Prove: If $S_{n}=S_{m}$ holds for some $m \neq n$, then $S_{n+m}=0$.
$$
S_{n}=\log a_{1}+\log a_{2}+\ldots+\log a_{n-1}+\log a_{n}
$$
Prove: If $S_{n}=S_{m}$ holds for some $m \neq n$, then $S_{n+m}=0$.