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  • 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'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'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"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'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'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"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

點與點之間的區別是什麼?

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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
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