Log of products to sum of logs rule

Questions
1

Hi,

A question to more experienced Mathematica users. Is there a standard way to convert Log of products to the product of logs with the indexed product and indexed sums?

Here’s the code I’m using for now but was wondering if there’s a way to achieve this with standard Mathematica built-in functions.

Open in Wolfram Cloud ↗

Please advise if you know of a better or more idiomatic Mathematica way.

2

That method looks fine. Not sure any alternative will improve on it, though often enough people surprise me in this respect.