# Quod Erat Demonstrandum

## 2010/04/16

### 問題在那裡？

＂express the answer in positive indices＂

O.T. 致：濟記同學

## 3 則迴響 »

1. 的確, 中三的課程對 laws of indices 基本上是隻字不提的.
一年不見, 難免生疏……

迴響 由 joesir — 2010/04/19 @ 3:14 下午 | 回應

2. John Sir:

“明白今時今日，中學同學對數學的興趣每下愈況”

努力！共勉

迴響 由 Eric — 2010/04/19 @ 9:14 下午 | 回應

3. “…用「連續性」一言以敝之，行嗎…"
Taking derivative is the same as finding a limit. So, you are suggesting the interchange of position of two limits. It may work if we can show the uniform convergence on the LHS.

With a subtle consideration of the branch of the complex logarithm (e.g. we cut a part of the imaginary axis to make logarithm well defined and hence differentiable in the domain), the power rule also works even if the base and the exponent are imaginary. The proof stated in your link actually works in the most general case.

迴響 由 Matt — 2010/04/24 @ 10:21 下午 | 回應