(log3^2 + log9^4)×(log4^3 + log8^3)
问题描述：
(log3^2 + log9^4)×(log4^3 + log8^3)
答
(log3 2+log9 4)*(log4 3+log8 3)
=(lg2/lg3+lg4/lg9)*(lg3/lg4+lg3/lg8)
=(lg2/lg3+2lg2/2lg3)*(lg3/2lg2+lg3/3lg2)
=(3lg2/lg3)*(lg3/2lg2+lg3/3lg2)
=(3lg2/lg3)*(3lg3/6lg2+2lg3/6lg2)
=(3lg2/lg3)*(5lg3/6lg2)
=3*5/6
=5/2
答
首先解释一下ln4=2ln2
底数也有类似规律
log4^3=1/2（log2^3）
所以
(log3^2 + log9^4)×(log4^3 + log8^3)
= (log3^2 + log3^2)×(（1/2）log2^3 + （1/3）log2^3)
=5/3