（1）计算：5x-23y12(-14x-1y12)(-56x12y-16)；（2）已知log53=a，log52=b，用a，b表示log2512．

Question

（1）计算：(5x-(2)/(3)y(1)/(2))/((-(1)/(4)x-1y(1)/(2))(-(5)/(6)x(1)/(2)y-(1)/(6)))；
（2）已知log₅3=a，log₅2=b，用a，b表示log₂₅12．

Answer 1

（1）(5x-(2)/(3)y(1)/(2))/((-(1)/(4)x-1y(1)/(2))(-(5)/(6)x(1)/(2)y-(1)/(6)))
=5×(-4)×(-(6)/(5))×x-(2)/(3)+1-(1)/(2)×y(1)/(2)-(1)/(2)+(1)/(6)
=24x-(1)/(6)y(1)/(6)．
（2）∵log₅3=a，log₅2=b，
∴log2512=(log512)/(log525)=(log53+2log52)/(2)=(a+2b)/(2)．