已知:12的x次幂=3,12的y次幂=2,求8的1-2y/1-x+y 已知:12的x次幂=3,12的y次幂=2,求8的1-2y/1-x+y

已知:12的x次幂=3,12的y次幂=2,求8的1-2y/1-x+y 已知:12的x次幂=3,12的y次幂=2,求8的1-2y/1-x+y

12^x=3 x=log12(3)
12^y=2 y=log12(2)
(1-2y)/(1-x+y)
=[1-2log12(2)]/[1-log12(3)+log12(2)]
=[log12(12/4)]/[log12(12×2/3)]
=[log12(3)]/[log12(8)]
=(lg3/lg12)/(lg8/lg12)
=lg3/lg8
=log8(3)
8^[(1-2y)/(1-x+y)]
=8^[log8(3)]
=3