Re: [中學] 指對數
※ 引述《dayjay (The last of us)》之銘言：
: 1/2 1/4 1/2
: log [ (x) + (x) ] = log (x)
: 12 9
: x 為正數，請求出x的值=? 用硬套的可以知道x=81
: 想知道有沒有比較仔細的分析 或是有其他解?
(log(x^(1/4)*(1+x^(1/4))))/log(12)=log(x^(1/2))/log(9)
Let y=x^(1/4)
Then x^(1/2)=y^2
(log(y)+log(1+y))/(log(12))=(2*log(y))/(2*log(3))
log(12)*log(y)=log(3)*(log(y)*(1+y))
If (y*(1+y)=3) And (y=12) Then NULL
If (y*(1+y)=12) And (y=3) Then y=3
y=3 => x=81
Reference:
(1) log[a](b)=log(a)/log(b)
(2) log(a*b)=log(a)+log(b)
(3) log(a^b)=b*log(a)
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※ 編輯: angel07 (61.231.93.119), 01/21/2016 12:32:27
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