注：文章内容来源于网络，真实性有待确认，请自行甄别。
对数若log(14)7=a,log(14)5=b,求log(35
发表于：2024-10-24 00:00:00浏览：6次
问题描述：若log()7=a,log(14)5=b,求log(35)28的值
log 7 = lg 7 / lg 14
log 14 5 = lg 5 / lg 14
A = lg 7 / lg 14 = lg 7 / (lg 7 + lg 2)
B = lg 5 / lg 14 = (1 - lg2) / (lg 7 + lg 2)
通过以上两式可得:
lg 7 = A / (1 - A + B)
lg 2 = (1 - A) / (1 - A + B)
log 35 28
= lg 28 / lg 35
= (lg 7 + 2lg 2) / (lg 7 + lg 5)
= (lg 7 + 2lg 2) / (lg 7 + 1 - lg2)
= [A / (1 - A + B) + 2(1 - A) / (1 - A + B)] / [A / (1 - A + B) + 1 - (1 - A) / (1 - A + B)]
= [(2 - A) / (1 - A + B)] / [(A + B) / (1 - A + B)]
= (2 - A) / (A + B)
猜你喜欢
栏目分类全部>