已知60^a＝3,60^b＝5,求12^{(1-a-b)/[2(1-b)]}
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已知60^a＝3,60^b＝5,求12^{(1-a-b)/[2(1-b)]}
已知60^a＝3,60^b＝5,求12^{(1-a-b)/[2(1-b)]}
已知60^a＝3,60^b＝5,求12^{(1-a-b)/[2(1-b)]}
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
a=log(60)3
b=log(60)5
a+b=log(60)3*5=log(60)15
1-(a+b)=log(60)(60/15)=log(60)4
1-b=log(60)(60/5)=log(60)12
2(1-b)=2log(60)12=
所以(1-a-b)/[2(1-b)]
=log(60)4/2log(60)12
=(...
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a=log(60)3
b=log(60)5
a+b=log(60)3*5=log(60)15
1-(a+b)=log(60)(60/15)=log(60)4
1-b=log(60)(60/5)=log(60)12
2(1-b)=2log(60)12=
所以(1-a-b)/[2(1-b)]
=log(60)4/2log(60)12
=(lg4/lg60)/(2lg12/lg60)
=(1/2)log(12)4
所以12^{(1-a-b)/[2(1-b)]}
=12^[(1/2)log(12)4]
=12^(1/2)*12^log(12)4
=(√12)*4
=8√3
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