## Subtitles section Play video

• 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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