log eqt 一問

2009-12-24 5:47 am
我想問點prove


a ^ (log(base a) x) =x ?

回答 (1)

2009-12-24 5:52 am
✔ 最佳答案
LHS take log first :

log { a ^ (log(base a) x) }
= log { a ^ (log x / log a) }
= (log x / log a) log a
= log x
So :

log { a ^ (log(base a) x) } = log x
a ^ (log(base a) x) = x


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