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  • How does the difference between point

  • 0-0-0-0-0-0-0-3-9-8

  • and point 0-0-0-0-0-0-0-0-3-9-8

  • cause one to have red eyes after swimming?

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

  • or in some cases extremely large numbers.

  • This leads us to the concept of logarithms.

  • Well, what are logarithms?

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

  • like 2 to the 3rd power

  • and have it equal a number n.

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

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

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

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

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

  • so let's show this with an example.

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

  • The same question could be asked using exponents.

  • 10 raised to what power is 10 thousand?

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

  • must equal 4.

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

  • Log base 10 is used so frequently in the sciences

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

  • If the calculator will figure out logs for me,

  • why study them?

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

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

  • So what is log base 2 of 64?

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

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

  • So log base 2 of 64 must equal 6.

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

  • in some swimming pools and not others?

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

  • finding the pH of water samples.

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

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

  • of the hydrogen ion concentration, or H plus.

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

  • point 0-0-0-0-0-0-0-3-9-8

  • and point 0-0-0-0-0-0-0-0-3-9-8

  • quickly on a calculator. Punch:

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

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

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

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

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

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

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

  • So now we know logarithms are very powerful

  • when dealing with extremely small or large numbers.

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

How does the difference between point

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B1 TED-Ed base log raised power calculator

【TED-Ed】Logarithms, Explained - Steve Kelly

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    Why Why posted on 2013/03/28
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