一道高一数学课本上的题最近在预习新高一的课本,在第二章对数函数时遇到了问题.(log3+log3)(log2+log2)利用对数的换底公式化简下列各式.*中的数字为对数的底数答案应该是5/4希望能发些详尽过程.

原式=(log3/log4+log3/log8)×(log2/log3+log2/log9)
=5/6 log3 × 3/2 log2
=5/4 log2
=5/4

(log3+log3)(log2+log2)
=[1/2*log3+1/3*log3][log2+1/2*log2]
=5/6*log3*3/2*log2
=5/4

题都不太看得明白.

原式=[1/2log3+1/3log3][log2+1/3log2]
=5/6log3*4/3log2
=10/9.......题目是不是打错了?

log2=log2=lg2/lg(3^2)=lg2/(2*lg3)=0.5*log2
同理 原式=5/6 *log3 *3/2*log2
=5/4