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# [Core] log 唔識做

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## log 唔識做

thx

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 ehbb 版主 發短消息 加為好友 當前離線 2# 大 中 小 發表於 2020-3-19 09:22 AM (第 189 天) 只看該作者 i) log_9 p = log(p)/log9 ii) log_12 q = log(q)/log12 iii) log_16 (p+q) = log(p+q)/log16 = log(p)+log(q)/log16 既然大家相等 即log(p)/log9 = log(q)/log12 = log(p)+log(q)/log16 咁樣做唔做到? UID221576 帖子2475 精華0 積分146 閱讀權限100 在線時間2976 小時 註冊時間2011-6-6 最後登錄2020-9-24  查看詳細資料 TOP
##### 引用:

i) log_9 p = log(p)/log9
ii) log_12 q = log(q)/log12
iii) log_16 (p+q) = log(p+q)/log16 = log(p)+log(q)/log16

(iii) is incorrect. The relation is "log (pq) = log p + log q". Can't just expand log (p+q) into log p + log q.
Sidenote, "(log p)/(log q) = log (p/q)" is not correct either.

The question looks very weird. The only lead I have is log9 + log16 = 2log12 (Go proof it!). So far no manipulation seems useful.

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##### 引用:

i) log_9 p = log(p)/log9
ii) log_12 q = log(q)/log12
iii) log_16 (p+q) = log(p+q)/log16 = log(p)+log(q)/log16

(iii) is incorrect. The relation is "log (pq) = log p + log q". Can't just expand log (p+q) into log p + log q.
Sidenote, "(log p)/(log q) = log (p/q)" is not correct either.

The question looks very weird. The only lead I have is log9 + log16 = 2log12 (Go proof it!). So far no manipulation seems useful.

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 風之男 學院師父 發短消息 加為好友 當前離線 5# 大 中 小 發表於 2020-3-21 02:24 AM (第 187 天) 只看該作者 The solution in #2 is incorrect. log (p+q) =/= log p + log q; log(pq) = log p + log q is the correct relation. So this question is very weird, but the major breakthrough for me is, surprisingly, going back to the definition of logarithms. (embed the image to the solution in just a sec) UID216418 帖子904 精華0 積分112 閱讀權限40 在線時間811 小時 註冊時間2011-5-4 最後登錄2020-9-24  查看詳細資料 TOP
 風之男 學院師父 發短消息 加為好友 當前離線 6# 大 中 小 發表於 2020-3-21 02:25 AM (第 187 天) 只看該作者 The solution in #2 is incorrect, can't quote for some reason. Remember only log(pq) = log p + log q. Can't do anything with log(p+q) So this question is quite difficult. The major "aha" moment for me is to consider the definition of logarithms. Also surprise! It's the golden ratio (or its buddy, I can't remember). Sorry for the huge image lmao. Message me for any queries. Good luck! [ 本帖最後由 風之男 於 2020-3-21 02:47 AM 編輯 ] 本帖最近評分記錄 ehbb 論壇積分 +3 敢於指正, 用心回應, 詳盡回覆 2020-3-21 10:07 AM UID216418 帖子904 精華0 積分112 閱讀權限40 在線時間811 小時 註冊時間2011-5-4 最後登錄2020-9-24  查看詳細資料 TOP

## 回覆 3# 風之男 的帖子

thx
very detail

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