How can I control the following behavior of Reduce?

Consider the following 3 lines of code:

Reduce[1. Log[3 - x] + 2. Log[1 + x] == 2.1972245773362196, x]
Reduce[1. Log[3 - x] + 2. Log[1 + x] == 2.1972245773362196 && x < 2, x]
Reduce[1. Log[3 - x] + 2. Log[1 + x] == 2.19722 && x < 2, x]

Which give the following output (and warning about exact representation which I have not included here)

Reduce[1. Log[3 - x] + 2. Log[1 + x] == 2.19722, x]

x == 1.30278 || x == 2.

x == 1.30276

Is there something I can change so that these give results that are more in line?

• I am particularly interested in making the 2nd the the third agree (since x==2 does not satisfy x<2)

I realize this is likely an issue of precision. My difficulty is that the numbers (1.,2.,2.19722…) are coming from earlier parts of code (i.e. I am not manually entering such numbers).

Perhaps if I tell mathematica to work with a certain level of precision (somehow keep it exact, or maybe use SetPrecision?) the discrepancy will be resolved?

• If so, is there I way I can tell mathematica to set precision locally (only for part of my notebook)?

Reduce[1. Log[3 - x] + 2. Log[1 + x] == 2.1972245773362196 && x < 2, x] //
 Style[#, PrintPrecision -> 17] &
Reduce[1. Log[3 - x] + 2. Log[1 + x] == 2.19722 && x < 2.1, x] // 
 Style[#, PrintPrecision -> 17] &

(*
  x == 1.3027756377319955 || x == 1.9999999999999993
  x == 1.30275925064097   || x == 2.000013731662965
*)