高中对数题
log以a为底18的对数等于M log以a为底24的对数等于N 请用M,N 表示log以a为底1.5的对数,求详细过程?
人气：390 ℃ 时间：2020-04-16 01:30:03
解答
M=log(a,18) N=log(a,24)M=log(a,2*3^2)=log(a,2)+2log(a,3)N=log(a,2^3*3)=3log(a,2)+log(a,3)所以log(a,2)=(2N-M)/5 log(a,3)=(3M-N)/5所以log(a,1.5)=log(a,3/2)=log(a,3)-log(a,2)=(3M-N-2N+M)/5=(4M-3N)/5
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