Log₃135/log₁₅3-log₃5/log₄₀₅3=log₃135/(1/log₃15)-log₃5/(1/log₃405)=
=log₃135*log₃15-log₃5*log₃405=log₃(27*5)*log₃(3*5)-log₃5*log₃(81*5)=
=(log₃27+log₃5)(log₃3+log₃5)-log₃5*(log₃81+log₃5)=
=(3+log₃5)(1+log₃5)-log₃5*(4+log₃5)=
=3+log₃5+3*log₃5+(log₃5)²-4*log₃5-(log₃5)²=
=3+4log₃5-4log₃5=3;
[(3+log₁₂27)/(3-log₁₂27)]*log₆16=[(3+3log₁₂3)/(3-3log₁₂3)]*log₆16=
=[3(1+log₁₂3)/3(1-log₁₂3)]*4*log₆2=(log₁₂12+log₁₂3)/(log₁₂12-log₁₂3)*log₆16=
=(log₁₂36/log₁₂4)*log₆16=
=[(log₂36/log₂12)/(log₂4/log₂12)]*log₂16/log₂6=
=(log₂36/log₂4)*log₂2⁴/log₂6=(2log₂6/2log₂2)*(4*log₂2/log₂6)=
=log₂6*4/log₂6=4;