已知60^a＝3,60^b＝5,求12^{(1-a-b)/[2(1-b)]}

题目

已知60^a＝3,60^b＝5,求12^{(1-a-b)/[2(1-b)]}

答案

60^a=3所以log60(a)=3
60^b=5所以log60(b)=5
1-a-b=log60(60)-log60(3)-log60(5)
=log60[60/(5*3)]=log60(4)
2(1-b)=2[log60(60)-log60(5)]
=2log60(60/5)
=2log60(12)
=log60(144)
(1-a-b)/[2(1-b)]=log60(4)/log60(144)=
=[lg(4)/lg(60)]/[lg(144)/lg(60)]=lg(4)/lg(144)=log144(4)
=0.5*log12(4)=log12(2)
12^{(1-a-b)/[2(1-b)]}=12^[log12(2)]
=2