Question

[log(4)3+log(8)3][log(3)2+log(9)2]

Answer 1

=[(log2 3)/2+(log2 3)/3][log3 2+(log3 2)/2]
=5/6×3/2×lod2 3×log3 2
=5/4

Answer 2

[log(4)3+log(8)3][log(3)2+log(9)2]
=(lg3/lg4+lg3/lg8)(lg2/lg3+lg2/lg9)
=[lg3/(2lg2)+lg3/(3lg2)][lg2/lg3+lg2/(2lg3)]
=(5/6)(lg3/lg2)(3/2)(lg2/lg3)
=(5/6)(3/2)
=5/4

Answer 3

运用换底公式。原式=【（ln3/ln4）+（ln3/ln8）】【（ln2/ln3）+（ln2/ln9）】
=【（ln3/2ln2）+（ln3/3ln2）】【（ln2/ln3）+（ln2/2ln3）】
=ln3/ln2*（1/2+1/3）*ln2/ln3*（1+1/2）
=5/6*3/2
=5/4

Answer 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]
=(5/6)(lg3/lg2)(3/2)(lg2/lg3)
=(5/6)(3/2)
=5/4

明白吗？用换底公式！

Answer 5

是4的三次方吗？