Re: [中學] 對數問題
※ 引述《aaaasd ()》之銘言：
: 已知a、b、c三數成等比
: 且log b、log c、log a三數成等差 求公差?
: a b c
: 思考很久 卻不得其解
: 懇求各位數學高手解答 非常謝謝
if a = b = c (滿足對數條件) , 公差為 0
假設不為 0
公比 r , 公差 d
a , b , c => b/r , b , br
log b = y-d , log c = y , log a = y+d
a b c
y y y-1
c = b => br = b => r = b
y-d y-d (2-y)(y-d)
b = a => b = (b/r) => b = b
=> (2-y)(y-d) = 1 (1)
y+d y+d 2-y y(y+d)
a = c => (b/r) = (br) => b = b
=> y(y+d) = 2 - y (2)
by (1) (2)
=> d = -3/2 ( y ≠ 1 )
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