如標題
題目如下:
5的X次方-3的X次方=5的X+1次方-3的X+1次方
答案為:log3/5為底的2
為什麼呢?????
log的相關問題!!!
2010-04-25 1:05 am
回答 (2)
2010-04-25 1:22 am
✔ 最佳答案
5^x - 3^x = 5^(x+1) - 3^(x+1)5^x - 5^(x+1) = 3^x - 3^(x+1)
5^x - 5(5^x) = 3^x - 3(3^x)
(5^x)(1 - 5) = (3^x)(1 - 3)
2(5^x) = 3^x
2 = (3/5)^x
log 2 = x log (3/5)
x = log2 / log (3/5)
x = log(3/5) 2
x = log3/5為底的2
2010-04-25 1:28 am
5的X次方-3的X次方=5的X+1次方-3的X+1次方
5^x - 3^x = 5^(x+1) - 3^(x+1)
5^x - 3^x = 5(5^x) - 3(3^x)
5^x - 3^x = 3(5^x - 3^x) + 2(5^x)
-2(5^x) = 2(5^x-3^x)
-5^x = 5^x - 3^x
3^x = 2(5^x)
log3^x = log2(5^x)
xlog3 = log2 + xlog5
x(log3-log5) = log2
x = log2/(log3/5)
x = log_3/5 2
5^x - 3^x = 5^(x+1) - 3^(x+1)
5^x - 3^x = 5(5^x) - 3(3^x)
5^x - 3^x = 3(5^x - 3^x) + 2(5^x)
-2(5^x) = 2(5^x-3^x)
-5^x = 5^x - 3^x
3^x = 2(5^x)
log3^x = log2(5^x)
xlog3 = log2 + xlog5
x(log3-log5) = log2
x = log2/(log3/5)
x = log_3/5 2
參考: Hope can help you^^”
收錄日期: 2021-04-21 22:10:20
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100424000015KK06124