maths log 問題

2008-03-05 7:05 am
設x>y>0,若log(x+y)=a and log(x-y)=b
則log 開方 x^2 -y^2= ?
p.s.開方成舊的
更新1:

thx,天日比你5分^^

回答 (1)

2008-03-05 7:15 am
✔ 最佳答案
log(x+y)=a
log(x-y)=b


log { x^2 -y^2 }^1/2   因 log x^y = y log x
=1/2 log { x^2 -y^2 }   因 x^2-y^2 = (x+y)(x-y)
=1/2 log { (x+y)(x-y) }  因 log a*b = loga+logb
=1/2 { log(x+y) + log(x-y) }
=1/2 ( a+b )#


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