LOG 99 = 1996/1000.

Quick bit of research revealed that while the Romans had neither fractions (as we know them) nor decimal points (nor place values, for that matter), they did have expressions for certain parts of whole. In particular, they had words for 1/12, 1/24, 1/48, 1/72, 1/144, and 1/288. The names for the latter three are very similar according to one source, unfortunately, searching on the word for 1/72 (scriptulum), I was informed by several other sites that that word actually meant 1/288.

Whichever word it was, the Romans had a system for "one off", by putting a prefix like "de" in the front, it would mean one 1/72 off the whole, which would mean 11/72. In this case, whichever that word was, one plus that fraction would be the closest approximation to log₁₀ 99.

Well, it would be if they'd had logarithms.

Sure! If they actually had them, I'd love for you to post a link in the comment section! Thank you for asking!