To log a specific signal in a ModelSim simulation, make a script like this:
view list add list -hex /tb_name/dut/signalname configure list -usestrobe 1 configure list -strobestart {<time> ns} -strobeperiod {<period> ns} configure list -usesignaltrigger 0 configure list -delta none configure list -usegating 1 configure list -gateexpr { /tb_name/dut/rst_n=='1' } write list -window .list <output_filename.log>