I am doing some assignments of an institute in which I dont study in complex analysis .
I am looking for verification of following proof and if its incorrect kindly give correct proof .
Prove that $\prod_{n=1}^{\infty} z_n $ converges if and only if $\sum_{n=1}^{\infty} log(z_n)$ converges.
Attempt :$\prod_{n=1}^{\infty} z_n $ converges to k iff $\sum_{n=1}^{\infty} log(z_n)$ converges to log k .
Is it fine ?