(log23+log92)(log43+log83)第一个数字是下标,

=log2 3 log4 3 + log 2 3 log 8 3 + log 9 2 log 4 3 + log 9 2 log 8 3
= 1/2 (log2 3)^2 + 1/3( log2 3)^2 + 1/2 log 3 2 *1/2log 2 3 + 1/2 log 3 2 * 1/3 log 2 3
= 5/6 (log 2 3)^2+1/4 + 1/6
=5/6 (log2 3)^2 + 5/12
= 2.51

(log23+log32/2)(log23/2+log23/3)=(log23+log32/2)5log23/6=5/6log23log23+5/12

（log(2)3+log(9)2)+(log（4）3+log(8)3)= （log(2)3+1/2log(3)2)(1/2log(2)3+1/3log(2)3)=（log(2)3+1/2log(3)2) *5/6log(2)3=（ln3/ln2+1/2 ln2/ln3)*5/6 ln3/ln2=5/6 log(2)3*log(2)3+5/12

=（log23+2log23）（1/2log32+1/3log32）=3log23*5/6log32=5(log23)^2/2

是不是：
[log3(2)＋log9(2)][log4(3)＋log8(3)]
＝[log3(2)＋1/2log3(2)][1/2log2(3)＋1/3log2(3)]
＝log3( 2•2^(1/2) )×log2( 3^(1/2)•3^(1/3) )
＝[3/2log3(2)]×[5/6log2(3)]
＝5/4