（1）计算：2log32-log3329+log38-25log53．（2）已知x=27，y=64．化简并计算：5x−23y12(−14x−1y12)(−56x13y−16)．

Question

（1）计算：2log₃2-log₃(32)/(9)+log₃8-25^log53．
（2）已知x=27，y=64．化简并计算：(5x−(2)/(3)y(1)/(2))/((−(1)/(4)x−1y(1)/(2))(−(5)/(6)x(1)/(3)y−(1)/(6)))．

Answer 1

（1）2log₃2-log₃(32)/(9)+log₃8-25^log53．
=log₃4-log₃(32)/(9)+log₃8-5^2log53
=log₃（4×(9)/(32)×8）-5^log59
=log₃9-9=2-9=-7．
（2）∵x=27，y=64，
∴(5x−(2)/(3)y(1)/(2))/((−(1)/(4)x−1y(1)/(2))(−(5)/(6)x(1)/(3)y−(1)/(6)))
=(5x−(2)/(3)y(1)/(2))/((−(1)/(4))×(−(5)/(6))×x−1+(1)/(3)×y(1)/(2)−(1)/(6))
=(5x−(2)/(3)•y(1)/(2))/((5)/(24)×x−(2)/(3)×y(1)/(3))
=24y (1)/(6)
=24×（2⁶） (1)/(6)
=48．