5^a=2^b=10^c
求(c/a)+(c/b)
要步驟,中文解釋
數學問題,數學問題,數學問題
2009-09-30 5:53 am
回答 (2)
2009-09-30 5:59 am
✔ 最佳答案
5^a = 2^b = 10^c
a log5 = b log2 = c log10
a log5 = b log2 = c
c/a + c/b
= (a log5 / a) + (b log2 / b)
= log 5 + log 2
= log 10
= 1
2009-09-30 9:07 am
對付對稱的問題 , 用對稱的方法
let 5^a=2^b=10^c = k
5^a= k => a = (log k) / (log 5)
2^b= k => b = (log k) / (log 2)
10^c= k => c = (log k) / (log 10)
(c/a)+(c/b)= {(log 5)/(log 10)} + {(log 2)/(log 10)}
= {(log 10)/(log 10)} = 1 (OR just use calculator)
let 5^a=2^b=10^c = k
5^a= k => a = (log k) / (log 5)
2^b= k => b = (log k) / (log 2)
10^c= k => c = (log k) / (log 10)
(c/a)+(c/b)= {(log 5)/(log 10)} + {(log 2)/(log 10)}
= {(log 10)/(log 10)} = 1 (OR just use calculator)
收錄日期: 2021-04-23 23:21:05
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090929000051KK01511