已知log5(3)=a,log5(4)=b,试用a,b表示log36(9).求详细过程~~

2024-11-16 17:49:23
推荐回答(3个)
回答(1):

log36(9)=log5(9)/log5(36)
=2log5(3)/[log5(4x9)]
=2a/[log5(4)+log5(9)]
=2a/(b+2a)

回答(2):

换底log36(9)=log5(36)/log5(9)=2log5(3)+log5(4)/2log5(3)=2a+b/2a

回答(3):

lg3/lg5=a,2lg2/lg5=b2lg6/2lg3=(lg3+lg2)/lg3=1+lg2/lg3b/a=2lg2/lg3lg2/lg3=b/2a2lg6/2lg3=(lg3+lg2)/lg3=1+lg2/lg3=1+b/2a