已知log4(27)=a,log5(2)=b,求lg2及lg3

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已知log4(27)=a,log5(2)=b,求lg2及lg3已知log4(27)=a,log5(2)=b,求lg2及lg3已知log4(27)=a,log5(2)=b,求lg2及lg3log4(27

已知log4(27)=a,log5(2)=b,求lg2及lg3
已知log4(27)=a,log5(2)=b,求lg2及lg3

已知log4(27)=a,log5(2)=b,求lg2及lg3
log4(27)=3/2log2(3)=a,
既log2(3)=2a/3.
既lg2/lg3=2a/3,
log5(2)=log2(2)/log2(5)
=1/[-1+1+log2(5)]
=1/[-1+log2(2)+log2(5)]
=1/{-1+log2(2*5)]=b,
log2(10)=(1+b)/b,
lg10/lg2=(1+b)/b,
lg2=b/(1+b),
代入上面的式子得到lg3=3b/(2a+2ab).