lg4+2lg5=lg4+lg5^2=lg4+lg25=lg(4*25)=lg100=2

lg500-lg5=lg(500/5)=lg100=2

log 42(2)+log42(3)+log42(7)=log42(2*3*7)=log42(42)=1

2log6(3)+log6(24)=log6(9)+log6(24)=log6(9*24)=log6(216)=3

log16(32)-log81(243)=log16(8)+log16(4)-(log81(81)+log81(3))=log16(4)+log16(2)+log16(4)-(log81(81)+log81(3))=0,5+0,25+0,5-1-0,25=0