用换底公式简化[log(4)3+log(8)3][log(3)2+log(9)2]比人还在自学期间,越清楚越明白越好~

[log(4)3+log(8)3][log(3)2+log(9)2]
=[2log(2)3+3log(2)3][log(3)2+2log(3)2]
=5log(2)3*3log(3)2
=5log(2)3*3/log(2)3
=15

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

[log(4)3+log(8)3][log(3)2+log(9)2]
=[1/2log(2)3+1/3log(2)3]*[log(3)2+1/2log(3)2]
=5/6log(2)3*3/2log(3)2
=5/4