已知log(a,18)=m,log(a,24)=n,用含有m,n的式子把log(a,1.5)表示出来._数学解答

已知log(a,18)=m,log(a,24)=n,用含有m,n的式子把log(a,1.5)表示出来.

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解答

log(a,18)=log(a,2)+2log(a,3)=m
log(a,24)=3log(a,2)+log(a,3)=n
求出log(a,2)=(2n-m)/5,log(a,3)=(3m-n)/5
log(a,1.5)=log(a,3)-log(a,2)=(3m-n)/5-(2n-m)/5=(4m-3n)/5