对数问题..

来源：百度知道 编辑：UC知道 时间：2024/07/05 13:59:42
log以8为底 3 =a
log以3为底 5 =b
求lg5用ab表示

log(3,8) = a ..... lg3/lg8 = a .... 换底公式log(x,y) = lgx/lgy
log(5,3) = b ..... lg5/lg3 = b

a*b = lg5/lg8
= lg5/lg(2^3)
= lg/(3*lg2)
= lg5/[3*(1 - lg5)]
令 x = lg5
3ab = x/(1 - x)
3ab - 3ab*x = x
x = 3ab/(1 + 3ab)

lg5 = 3ab/(1 + 3ab)

楼上对的,就是lg5 = 3ab/(1 + 3ab)