## 字幕列表 影片播放

• How does the difference between point

點與點之間的區別是什麼？

• 0-0-0-0-0-0-0-3-9-8

0-0-0-0-0-0-0-3-9-8

• and point 0-0-0-0-0-0-0-0-3-9-8

和0-0-0-0-0-0-0-0-3-9-8點。

• cause one to have red eyes after swimming?

使人游泳後眼睛發紅？

• To answer this, we first need a way of dealing with rather small numbers,

要回答這個問題，我們首先需要一個處理相當小的數字的方法。

• or in some cases extremely large numbers.

或在某些情況下數量極多。

• This leads us to the concept of logarithms.

這就引出了對數的概念。

• Well, what are logarithms?

那麼，什麼是對數？

• Let's take the base number - b - and raise it to a power, p,

讓我們&#39;把基數--b--提高到一個冪，p。

• like 2 to the 3rd power

像2到3倍的力量

• and have it equal a number n.

並讓它等於一個數字n。

• We get an exponential equation b raised to the p power equals n.

我們得到一個指數方程b提高到p冪等於n。

• In our example, that'd be 2 raised to the 3rd power equals 8.

在我們的例子中，那&#39;d是2提高到3次方等於8。

• The exponent p is said to be the logarithm of the number n.

指數p被稱為是數字n的對數。

• Most of the time this would be written "log base b of a number equals p, the power."

大多數情況下，這會被寫成&quot;一個數的對數基數b等於p，冪.&quot。

• This is starting to sound a bit confusing with all the variables,

這開始聽起來有點混亂，所有的變量。

• so let's show this with an example.

所以讓我們&#39;用一個例子來說明。

• What is the value of log base 10 of 10 thousand?

萬的對數基數10的值是多少？

• The same question could be asked using exponents.

同樣的問題可以用指數來問。

• 10 raised to what power is 10 thousand?

10提高到什麼力量是1萬？

• Well, 10 to the 4th is 10 thousand. So, log base 10 of 10 thousand

好吧，10到4是1萬。所以，對數基數10的萬

• must equal 4.

必須等於4。

• This example can also be completed very simply on a scientific calculator.

這個例子也可以在科學計算器上非常簡單地完成。

• Log base 10 is used so frequently in the sciences

對數基數10在科學中使用頻率很高。

• that it has the honor of having its own button on most calculators.

它有幸在大多數計算器上擁有自己的按鈕。

• If the calculator will figure out logs for me,

如果計算器能幫我算出日誌。

• why study them?

為什麼要研究它們？

• Just a quick reminder, the log button only computes logarithms of base 10.

提醒一下，日誌按鈕只計算10基的對數。

• What if you want to go into computer science and need to understand base 2?

如果你想進入計算機科學領域，需要了解基數2怎麼辦？

• So what is log base 2 of 64?

那麼64的對數基數2是什麼呢？

• In other words, 2 raised to what power is 64?

換句話說，2提高到什麼功率是64？

• Well, use your fingers. 2, 4, 8, 16, 32, 64.

好吧，用你的手指。2, 4, 8, 16, 32, 64.

• So log base 2 of 64 must equal 6.

所以64的對數基數2一定等於6。

• So what does this have to do with my eyes turning red

這跟我眼睛變紅有什麼關係？

• in some swimming pools and not others?

在一些游泳池中，而不是在其他游泳池中？

• Well, it leads us into an interesting use of logarithms in chemistry:

好吧，這讓我們進入了一個有趣的化學中對數的應用。

• finding the pH of water samples.

尋找水樣的pH值。

• pH tells us how acidic or basic a sample is,

pH值告訴我們樣品的酸鹼度。

• and can be calculated with the formula pH equals negative log base 10

並可以用公式計算出pH值等於負對數鹼10

• of the hydrogen ion concentration, or H plus.

的氫離子濃度，即H加。

• We can find the pH of water samples with hydrogen ion concentration of

我們可以求出氫離子濃度為的水樣的pH值為

• point 0-0-0-0-0-0-0-3-9-8

0-0-0-0-0-0-3-9-8點

• and point 0-0-0-0-0-0-0-0-3-9-8

和0-0-0-0-0-0-0-0-3-9-8點。

• quickly on a calculator. Punch:

迅速在計算器上。衝。

• negative log of each of those numbers, and you'll see the pHs are 7.4 and 8.4.

這些數字的負對數，你&#39;會看到pH值是7.4和8.4。

• Since the tears in our eyes have a pH of about 7.4,

由於我們眼睛裡的淚水的pH值約為7.4。

• the H plus concentration of .70398 will feel nice on your eyes.

H加濃度為0.70398，眼睛會感覺很舒服。

• But the pH of 8.4 will make you feel itchy and red.

但pH值為8.4，會讓你覺得很癢，很紅。

• It's easy to remember logarithms - log base b of some number n

這很容易記住對數--某個數字n的對數基數b。

• equals p - by repeating "the base raised to what power equals the number?"

等於p--通過重複&quot;基數提高到多少倍等於多少?&quot。

• The base raised to what power equals the number? The base raised to what power equals the number?

基數提高到多少倍等於多少？基數提高到多少倍等於多少？

• So now we know logarithms are very powerful

所以現在我們知道了對數是非常強大的。

• when dealing with extremely small or large numbers.

當處理極小或極多的數字時。

• Logarithms can even be used instead of eyedrops after swimming.

游泳後甚至可以用對數代替眼藥水。

How does the difference between point

B1 中級 中文 TED-Ed 等於 數字 濃度 指數 眼睛

# 【TED-Ed】甚麼是"對數"(Logarithms, Explained - Steve Kelly)

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Why Why 發佈於 2013 年 03 月 28 日