用换底公试间化:loga c乘以logc a log2 3乘以log3 4乘以log4 5乘以log5 2 (log4 3+log8 3)(log3 2+log9 2)最好写下过程

loga c乘以logc a log2 3乘以log3 4乘以log4 5乘以log5 2 (log4 3+log8 3)(log3 2+log9 2)最好写下过程 是3道题

1)log(a)c×log(c)a

=(lgc/lga)×(lga/lgc)

=1

2)log(2)3×log(3)4×log(4)5×log(5)2

=(lg3/lg2)×(lg4/lg3)×(lg5/lg4)×(lg2/lg5)

=1

3)(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)]

=(1/2+1/3)(lg3/lg2)×(1+1/2)(lg2/lg3)

=(5/6)×(3/2)

=5/4

(lgc/lga)*lga/lgc=1 (lg3/lg2)*(lg4/lg3)=lg2 最后一题过程多.不过方法一样.依次类推