Question

高一数学对数运算

（log2 3+log4 27)(log3 4+log9 8)=_________
其中2、4、3、9为下标，
需要过程！！！！

Answer 1

利用对数的性质：t>0且t≠1
则：loga b=(logt b)/(logt a)【等号左边a是底数，右边t为底数】
log4 27 =(log2 3³)/(log2 4) =（3/2）log2 3
log9 8 =(log3 2³）/（log3 3²）=（3/2）log3 2
log3 4=2log3 2

（log2 3+log4 27)(log3 4+log9 8)
=(5/2)log2 3 *(7/2)log3 2
=(35/4)[(log2 3)/(log2 3)]
35/4

Answer 2

（log2 3+log4 27)(log3 4+log9 8)
=(LOG(2,3)+LOG(10,27)/LOG(10,4))(2LOG(3,2)+LOG(10,8)/LOG(10,9))
=(LOG(2,3)+(3/2)LOG(2,3))(2LOG(3,2)+(3/2)LOG(3,2)
=(5/2)LOG(2,3)*(5/2)/LOG(2,3)
=25/4