[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.99,0:00:03.75,Default,,0000,0000,0000,,歡迎觀看對數課程
Dialogue: 0,0:00:03.86,0:00:06.65,Default,,0000,0000,0000,,寫一寫“對數”這個詞
Dialogue: 0,0:00:06.65,0:00:08.57,Default,,0000,0000,0000,,這又是一個構造複雜的新單詞
Dialogue: 0,0:00:08.58,0:00:10.69,Default,,0000,0000,0000,,像“斜邊”
Dialogue: 0,0:00:10.69,0:00:14.48,Default,,0000,0000,0000,,最好看一下怎麽寫
Dialogue: 0,0:00:14.48,0:00:19.97,Default,,0000,0000,0000,,我先把筆調出來
Dialogue: 0,0:00:19.97,0:00:24.47,Default,,0000,0000,0000,,對數
Dialogue: 0,0:00:24.62,0:00:27.29,Default,,0000,0000,0000,,很容易拼錯
Dialogue: 0,0:00:27.30,0:00:30.05,Default,,0000,0000,0000,,我之前去MIT
Dialogue: 0,0:00:30.05,0:00:31.71,Default,,0000,0000,0000,,到那的一個阿卡貝拉團
Dialogue: 0,0:00:31.71,0:00:33.99,Default,,0000,0000,0000,,名叫Logarhythms
Dialogue: 0,0:00:33.99,0:00:35.72,Default,,0000,0000,0000,,像音樂旋律
Dialogue: 0,0:00:35.72,0:00:37.78,Default,,0000,0000,0000,,扯遠了
Dialogue: 0,0:00:37.78,0:00:41.35,Default,,0000,0000,0000,,對數是什麽？
Dialogue: 0,0:00:41.36,0:00:43.13,Default,,0000,0000,0000,,最容易理解的解釋
Dialogue: 0,0:00:43.14,0:00:44.24,Default,,0000,0000,0000,,是
Dialogue: 0,0:00:44.25,0:00:49.89,Default,,0000,0000,0000,,把它看成
Dialogue: 0,0:00:49.89,0:00:52.10,Default,,0000,0000,0000,,指數的逆運算
Dialogue: 0,0:00:52.11,0:00:54.76,Default,,0000,0000,0000,,舉例說明
Dialogue: 0,0:00:54.77,0:00:56.82,Default,,0000,0000,0000,,2的3次方
Dialogue: 0,0:00:56.82,0:00:59.52,Default,,0000,0000,0000,,指數部分已經學過
Dialogue: 0,0:00:59.53,0:01:04.57,Default,,0000,0000,0000,,2的3次方等於8
Dialogue: 0,0:01:04.57,0:01:13.19,Default,,0000,0000,0000,,重寫一下 這是2不是z
Dialogue: 0,0:01:13.20,0:01:15.12,Default,,0000,0000,0000,,2的3次方等於8
Dialogue: 0,0:01:15.12,0:01:17.19,Default,,0000,0000,0000,,由此得出log
Dialogue: 0,0:01:17.20,0:01:22.72,Default,,0000,0000,0000,,log表示對數
Dialogue: 0,0:01:22.73,0:01:27.76,Default,,0000,0000,0000,,log以2爲底8的對數等於3
Dialogue: 0,0:01:27.76,0:01:31.05,Default,,0000,0000,0000,,看看這個運算大家就明白
Dialogue: 0,0:01:31.06,0:01:33.87,Default,,0000,0000,0000,,怎麽由指數到對數
Dialogue: 0,0:01:33.87,0:01:36.43,Default,,0000,0000,0000,,也就是說
Dialogue: 0,0:01:36.43,0:01:42.30,Default,,0000,0000,0000,,log以2爲底8的對數等於幾
Dialogue: 0,0:01:42.31,0:01:43.96,Default,,0000,0000,0000,,相當於問 2的幾次方等於8？
Dialogue: 0,0:01:43.96,0:01:47.55,Default,,0000,0000,0000,,因此對數運算的結果
Dialogue: 0,0:01:47.56,0:01:54.68,Default,,0000,0000,0000,,也可以說對數表達式的結果
Dialogue: 0,0:01:54.68,0:02:03.69,Default,,0000,0000,0000,,或者說如果要算對數表達式
Dialogue: 0,0:02:03.70,0:02:09.80,Default,,0000,0000,0000,,應該算出
Dialogue: 0,0:02:09.81,0:02:14.21,Default,,0000,0000,0000,,2的指數爲幾的時候等於8
Dialogue: 0,0:02:14.22,0:02:16.78,Default,,0000,0000,0000,,爲3
Dialogue: 0,0:02:16.78,0:02:18.28,Default,,0000,0000,0000,,再做幾個例子大家就會理解
Dialogue: 0,0:02:18.28,0:02:20.95,Default,,0000,0000,0000,,log 筆怎麽了
Dialogue: 0,0:02:20.96,0:02:25.94,Default,,0000,0000,0000,,log以4爲底64的對數等於x
Dialogue: 0,0:02:25.94,0:02:36.11,Default,,0000,0000,0000,,這跟另一個式子意義相同
Dialogue: 0,0:02:36.12,0:02:39.31,Default,,0000,0000,0000,,4的x次方等於64
Dialogue: 0,0:02:39.31,0:02:42.24,Default,,0000,0000,0000,,換一個思路想
Dialogue: 0,0:02:42.25,0:02:45.71,Default,,0000,0000,0000,,4的幾次方等於64？
Dialogue: 0,0:02:45.71,0:02:48.96,Default,,0000,0000,0000,,大家知道4的3次方是64
Dialogue: 0,0:02:48.97,0:02:52.37,Default,,0000,0000,0000,,所以這裡答案是3
Dialogue: 0,0:02:52.38,0:03:05.77,Default,,0000,0000,0000,,log以4爲底64的對數等於3
Dialogue: 0,0:03:05.78,0:03:08.53,Default,,0000,0000,0000,,再多做幾個例子
Dialogue: 0,0:03:08.53,0:03:12.48,Default,,0000,0000,0000,,大家做的題越多
Dialogue: 0,0:03:12.49,0:03:15.95,Default,,0000,0000,0000,,就理解的更清楚
Dialogue: 0,0:03:15.96,0:03:17.77,Default,,0000,0000,0000,,對數是個簡單的概念
Dialogue: 0,0:03:17.77,0:03:22.05,Default,,0000,0000,0000,,但作爲指數的逆運算
Dialogue: 0,0:03:22.06,0:03:24.90,Default,,0000,0000,0000,,可能不好理解
Dialogue: 0,0:03:24.90,0:03:26.93,Default,,0000,0000,0000,,因爲指數也不好理解
Dialogue: 0,0:03:26.93,0:03:29.55,Default,,0000,0000,0000,,log以10爲底1000000的對數
Dialogue: 0,0:03:29.55,0:03:31.34,Default,,0000,0000,0000,,標上逗號
Dialogue: 0,0:03:31.34,0:03:34.58,Default,,0000,0000,0000,,等於幾
Dialogue: 0,0:03:34.59,0:03:47.16,Default,,0000,0000,0000,,這時候該思考的是
Dialogue: 0,0:03:47.16,0:03:54.05,Default,,0000,0000,0000,,10的幾次方是1000000
Dialogue: 0,0:03:54.06,0:03:57.74,Default,,0000,0000,0000,,10的幾次方等於
Dialogue: 0,0:03:57.74,0:03:59.63,Default,,0000,0000,0000,,1後面跟幾個0
Dialogue: 0,0:03:59.63,0:04:01.45,Default,,0000,0000,0000,,比如10的5次方
Dialogue: 0,0:04:01.46,0:04:04.19,Default,,0000,0000,0000,,就等於1後面跟5個0
Dialogue: 0,0:04:04.19,0:04:06.30,Default,,0000,0000,0000,,現在1後面有6個0
Dialogue: 0,0:04:06.31,0:04:08.83,Default,,0000,0000,0000,,也就是10的6次方
Dialogue: 0,0:04:08.83,0:04:12.56,Default,,0000,0000,0000,,所以10的6次方等於1000000
Dialogue: 0,0:04:12.56,0:04:19.78,Default,,0000,0000,0000,,因爲10的6次方等於1000000
Dialogue: 0,0:04:19.79,0:04:23.25,Default,,0000,0000,0000,,所以log以10爲底1000000的對數等於6
Dialogue: 0,0:04:25.81,0:04:27.74,Default,,0000,0000,0000,,記住
Dialogue: 0,0:04:27.75,0:04:32.04,Default,,0000,0000,0000,,6爲指數
Dialogue: 0,0:04:32.05,0:04:32.67,Default,,0000,0000,0000,,以10爲底得到1000000
Dialogue: 0,0:04:32.67,0:04:34.27,Default,,0000,0000,0000,,我用了很多種方法講解對數
Dialogue: 0,0:04:34.27,0:04:37.01,Default,,0000,0000,0000,,我希望
Dialogue: 0,0:04:37.01,0:04:40.49,Default,,0000,0000,0000,,這其中會有幾種
Dialogue: 0,0:04:44.49,0:04:54.76,Default,,0000,0000,0000,,能使大家清楚的理解對數
Dialogue: 0,0:04:54.76,0:04:56.26,Default,,0000,0000,0000,,再做幾個練習
Dialogue: 0,0:04:56.27,0:05:00.84,Default,,0000,0000,0000,,下面這個會難一點
Dialogue: 0,0:05:02.29,0:05:13.67,Default,,0000,0000,0000,,log以1/2爲底1/8的對數
Dialogue: 0,0:05:13.68,0:05:16.48,Default,,0000,0000,0000,,等於x
Dialogue: 0,0:05:16.48,0:05:20.51,Default,,0000,0000,0000,,大家回想一下
Dialogue: 0,0:05:20.51,0:05:22.78,Default,,0000,0000,0000,,這個等同於 1/2
Dialogue: 0,0:05:22.79,0:05:25.35,Default,,0000,0000,0000,,應該是括號
Dialogue: 0,0:05:34.06,0:05:36.17,Default,,0000,0000,0000,,1/2的x次方等於1/8
Dialogue: 0,0:05:36.17,0:05:38.16,Default,,0000,0000,0000,,我們知道1/2的3次方
Dialogue: 0,0:05:38.16,0:05:39.73,Default,,0000,0000,0000,,等於1/8
Dialogue: 0,0:05:39.74,0:05:41.36,Default,,0000,0000,0000,,所以log以1/2爲底1/8的對數等於3
Dialogue: 0,0:05:41.37,0:05:43.14,Default,,0000,0000,0000,,再多做幾個題目
Dialogue: 0,0:05:43.14,0:05:51.05,Default,,0000,0000,0000,,跟前面的不同
Dialogue: 0,0:05:51.06,0:05:54.10,Default,,0000,0000,0000,,log以x爲底27的對數等於3
Dialogue: 0,0:05:55.82,0:05:57.74,Default,,0000,0000,0000,,x等於幾？
Dialogue: 0,0:05:57.75,0:06:00.05,Default,,0000,0000,0000,,跟前面一樣
Dialogue: 0,0:06:00.05,0:06:07.70,Default,,0000,0000,0000,,這個等同於 x的3次方等於27
Dialogue: 0,0:06:07.70,0:06:14.43,Default,,0000,0000,0000,,或是x等於27的立方根
Dialogue: 0,0:06:14.43,0:06:16.68,Default,,0000,0000,0000,,也就是說一個數自乘3次後
Dialogue: 0,0:06:16.68,0:06:18.36,Default,,0000,0000,0000,,等於27
Dialogue: 0,0:06:18.37,0:06:22.43,Default,,0000,0000,0000,,大家知道
Dialogue: 0,0:06:22.43,0:06:25.31,Default,,0000,0000,0000,,這個數是3
Dialogue: 0,0:06:25.32,0:06:30.24,Default,,0000,0000,0000,,x等於3
Dialogue: 0,0:06:30.25,0:06:32.72,Default,,0000,0000,0000,,log以3爲底27的對數
Dialogue: 0,0:06:32.72,0:06:34.95,Default,,0000,0000,0000,,等於3
Dialogue: 0,0:06:34.95,0:06:37.51,Default,,0000,0000,0000,,再舉一個例子
Dialogue: 0,0:06:37.52,0:06:39.78,Default,,0000,0000,0000,,我們只用較小的數做練習
Dialogue: 0,0:06:39.79,0:06:42.47,Default,,0000,0000,0000,,因爲沒有計算器
Dialogue: 0,0:06:42.47,0:06:44.87,Default,,0000,0000,0000,,只能心算
Dialogue: 0,0:06:44.87,0:06:51.31,Default,,0000,0000,0000,,log 我先想想
Dialogue: 0,0:06:51.32,0:07:00.40,Default,,0000,0000,0000,,log以100爲底1的對數是幾？
Dialogue: 0,0:07:00.41,0:07:04.92,Default,,0000,0000,0000,,比較難
Dialogue: 0,0:07:04.93,0:07:07.86,Default,,0000,0000,0000,,再來一次
Dialogue: 0,0:07:07.86,0:07:16.11,Default,,0000,0000,0000,,假設等於問號
Dialogue: 0,0:07:16.12,0:07:18.05,Default,,0000,0000,0000,,是log以100爲底1的對數
Dialogue: 0,0:07:18.06,0:07:20.32,Default,,0000,0000,0000,,那麽100的問號次方
Dialogue: 0,0:07:20.32,0:07:22.15,Default,,0000,0000,0000,,等於1
Dialogue: 0,0:07:22.16,0:07:25.76,Default,,0000,0000,0000,,這時候應該想
Dialogue: 0,0:07:25.76,0:07:28.42,Default,,0000,0000,0000,,有沒有一個數作爲指數時
Dialogue: 0,0:07:28.43,0:07:30.57,Default,,0000,0000,0000,,結果爲1？
Dialogue: 0,0:07:30.57,0:07:32.84,Default,,0000,0000,0000,,大家記得指數法則中
Dialogue: 0,0:07:32.85,0:07:33.78,Default,,0000,0000,0000,,也不算是指數法則
Dialogue: 0,0:07:33.79,0:07:35.82,Default,,0000,0000,0000,,是指數某一節中的內容
Dialogue: 0,0:07:35.82,0:07:38.69,Default,,0000,0000,0000,,任何數的0次方都等於1
Dialogue: 0,0:07:38.70,0:07:41.98,Default,,0000,0000,0000,,所以100的0次方等於1
Dialogue: 0,0:07:41.99,0:07:44.43,Default,,0000,0000,0000,,log以100爲底1的對數
Dialogue: 0,0:07:44.43,0:07:51.30,Default,,0000,0000,0000,,等於0
Dialogue: 0,0:07:51.31,0:07:54.19,Default,,0000,0000,0000,,因爲100的0次方等於1
Dialogue: 0,0:07:54.20,0:07:56.80,Default,,0000,0000,0000,,再問一個問題
Dialogue: 0,0:07:56.81,0:07:58.62,Default,,0000,0000,0000,,log以2爲底0的對數是幾？
Dialogue: 0,0:07:58.62,0:08:00.43,Default,,0000,0000,0000,,等於多少？
Dialogue: 0,0:08:00.43,0:08:02.65,Default,,0000,0000,0000,,也就是
Dialogue: 0,0:08:02.66,0:08:04.23,Default,,0000,0000,0000,,假設等於x
Dialogue: 0,0:08:04.24,0:08:10.50,Default,,0000,0000,0000,,2的x次方等於0
Dialogue: 0,0:08:14.62,0:08:21.37,Default,,0000,0000,0000,,x是多少？
Dialogue: 0,0:08:21.37,0:08:23.67,Default,,0000,0000,0000,,有沒有2的幾次方
Dialogue: 0,0:08:23.68,0:08:25.58,Default,,0000,0000,0000,,可以等於0
Dialogue: 0,0:08:25.58,0:08:26.20,Default,,0000,0000,0000,,沒有 所以它不成立
Dialogue: 0,0:08:26.20,0:08:28.97,Default,,0000,0000,0000,,不成立或者說無解
Dialogue: 0,0:08:28.98,0:08:30.01,Default,,0000,0000,0000,,2的無論幾次方
Dialogue: 0,0:08:30.01,0:08:32.34,Default,,0000,0000,0000,,都不等於0
Dialogue: 0,0:08:32.35,0:08:36.38,Default,,0000,0000,0000,,類似的情況 log以3爲底
Dialogue: 0,0:08:36.38,0:08:39.23,Default,,0000,0000,0000,,-1的對數
Dialogue: 0,0:08:39.24,0:08:47.12,Default,,0000,0000,0000,,假設在實數範圍內
Dialogue: 0,0:08:47.12,0:08:52.49,Default,,0000,0000,0000,,到目前爲止
Dialogue: 0,0:08:52.50,0:08:53.93,Default,,0000,0000,0000,,大家接觸的大部分都是實數的運算
Dialogue: 0,0:08:53.94,0:09:00.00,Default,,0000,0000,0000,,那麽沒有3的幾次方
Dialogue: 0,0:09:00.00,0:09:02.78,Default,,0000,0000,0000,,等於負數 所以沒有定義
Dialogue: 0,0:09:02.79,0:09:06.23,Default,,0000,0000,0000,,因此只要對數底爲正數
Dialogue: 0,0:09:06.24,0:09:09.32,Default,,0000,0000,0000,,要使式子有意義這個數必須大於
Dialogue: 0,0:09:09.32,0:09:13.02,Default,,0000,0000,0000,,大於或等於 不對
Dialogue: 0,0:09:13.02,0:09:17.60,Default,,0000,0000,0000,,必須大於0
Dialogue: 0,0:09:17.61,0:09:20.23,Default,,0000,0000,0000,,不能等於0
Dialogue: 0,0:09:20.23,0:09:24.96,Default,,0000,0000,0000,,不能爲0或負數
Dialogue: 0,0:09:24.96,0:09:26.96,Default,,0000,0000,0000,,再做幾個特殊的題目
Dialogue: 0,0:09:26.96,0:09:29.58,Default,,0000,0000,0000,,還剩一分半鍾
Dialogue: 0,0:09:29.59,0:09:31.59,Default,,0000,0000,0000,,大家現在可以做
Dialogue: 0,0:09:31.59,0:09:33.83,Default,,0000,0000,0000,,難度1的對數題了
Dialogue: 0,0:09:33.83,0:09:36.25,Default,,0000,0000,0000,,我們再做幾個題
Dialogue: 0,0:09:36.25,0:09:38.87,Default,,0000,0000,0000,,log以8爲底
Dialogue: 0,0:09:38.87,0:09:43.11,Default,,0000,0000,0000,,稍難一點 1/64的對數是多少
Dialogue: 0,0:09:43.12,0:09:45.76,Default,,0000,0000,0000,,有趣
Dialogue: 0,0:09:45.76,0:09:47.59,Default,,0000,0000,0000,,大家知道log以8爲底64的對數等於2