log以3为底1/16的对数xlog以5为底1/9的对数怎么算
问题描述：
log以3为底1/16的对数xlog以5为底1/9的对数怎么算
答
log(a)(N)表示以a为底数，N为真数的对数形式
[log(3)(1/16)]*[log(5)(1/9)]
=[log(3)(2^(-4))]*[log(5)(3^(-2))]
=(-4)*(-2)*[log(3)(2)]*[log(5)(3)]
=8*(lg2/lg3)*(lg3/lg5)
=8(lg2/lg5)
=8log(5)(2)
答
答案：
log3(1/16) xlog5(1/9)
=(-4)log3(2)x(-2)log5(3)
=8lg2/lg3xlg3/lg2
=8lg3/lg2
=8log2(3)