Question

设log以3为底4的对数,乘以log以8为底M的对数,等于log以4为底16的对数,那么M等于多少?

Answer 1

D

首先化减:

log8(M)*log3(4)=log4(16)=2

log8(M)=2/log3(4)=log3(9)/log3(4)

运用换底公式

log3(9)/log3(4)=log4(9)

所以log8(M)=log4(9)

即log2^3(M)=log2^2(9)

然后把底数的次方数提到前面

即1/3log2(M)=1/2log2(9)

log2(M)=3/2log2(9)=log2(9^(3/2))=log2(27)

M=27