log(75÷16)-2log(5÷9)+log(32÷243)=log(2) [prove it]
log(75/16)-2log(5/9)+log(32/243)=log(2) = {} A.K.A. it doesn't.
Proof here.
2 log(9/5)+log(75/16)-log(243/32)=0.69314718055994530941.......etc=ln(2)
THEREFORE THE EQUALITY IS TRUE.
see: http://web2.0calc.com/questions/help-8-4#r1