己知8^x=0.08^y=1000
不求出x,y的值而求1/x-1/y
一條log既問題
2006-10-27 3:43 am
回答 (3)
2006-10-27 3:57 am
✔ 最佳答案
8^x = 1000x = log 1000 / log 8
1/x = log 8 / log 1000
1/x = log 8 / 3
0.08^y = 1000
y = log 1000 / log 0.08
1/y = log 0.08 / log 1000
1/y = (log 8 - log 100) / log 1000
1/y = (log 8 - 2) / 3
1/x-1/y = (log 8 - log 8 + 2) / 3
= 2 / 3
參考: my mathematical knowledge
2006-10-27 4:06 am
8^x=0.08^y=1000
log8^x=log0.08^y=log1000
xlog8=ylog0.08=log10^3
xlog8=log10^3
x=log10^3/log8
1/x=log8/3 Since log1000=3
ylog0.08=log10^3
y=log10^3/log0.08
1/y=log0.08/3 Since log1000=3
1/x-1/y=log8/3-log0.08/3
=log8-log0.08/3
=log(8/0.08)/3
=log100/3
=2/3
log8^x=log0.08^y=log1000
xlog8=ylog0.08=log10^3
xlog8=log10^3
x=log10^3/log8
1/x=log8/3 Since log1000=3
ylog0.08=log10^3
y=log10^3/log0.08
1/y=log0.08/3 Since log1000=3
1/x-1/y=log8/3-log0.08/3
=log8-log0.08/3
=log(8/0.08)/3
=log100/3
=2/3
2006-10-27 4:06 am
8 ^ x = 1000
x log 8 = log 1000
x = log 1000 / log 8
0.08 ^ y = 1000
y log 0.08 = log 1000
y = log 1000 / log 0.08
So. 1 / x - 1 / y
= 1 / ( log 1000 / log 8 ) - 1 / ( log 1000 / log 0.08 )
= log 8 / log 1000 - log 0.08 / log 1000
= ( log 8 - log 0.08 ) / 3
= 2 / 3 #
x log 8 = log 1000
x = log 1000 / log 8
0.08 ^ y = 1000
y log 0.08 = log 1000
y = log 1000 / log 0.08
So. 1 / x - 1 / y
= 1 / ( log 1000 / log 8 ) - 1 / ( log 1000 / log 0.08 )
= log 8 / log 1000 - log 0.08 / log 1000
= ( log 8 - log 0.08 ) / 3
= 2 / 3 #
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061026000051KK03502