Why a Precision problem for Floor of quotient of Logs?

This line returns a Precision problem:

Floor[Log[9]/Log[3]]

This one works fine:

Floor[Log[9]/Log[3]//N]

What I don't understand is why one works while the other doesn't because I assume that internally Mathematica would numerically evaluate the argument of Floor first anyway, so the two lines should be logically equivalent, the 2nd one just redundant. But clearly I was wrong. What did I misunderstand about how Floor works?