[Script Info]
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[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:15.00,0:00:18.00,Default,,0000,0000,0000,,How does the difference between point
Dialogue: 0,0:00:18.00,0:00:21.00,Default,,0000,0000,0000,,0-0-0-0-0-0-0-3-9-8
Dialogue: 0,0:00:21.00,0:00:24.00,Default,,0000,0000,0000,,and point 0-0-0-0-0-0-0-0-3-9-8
Dialogue: 0,0:00:24.00,0:00:28.00,Default,,0000,0000,0000,,cause one to have red eyes after swimming?
Dialogue: 0,0:00:28.00,0:00:31.00,Default,,0000,0000,0000,,To answer this, we first need a way of dealing with rather small numbers,
Dialogue: 0,0:00:31.00,0:00:34.00,Default,,0000,0000,0000,,or in some cases extremely large numbers.
Dialogue: 0,0:00:34.00,0:00:37.00,Default,,0000,0000,0000,,This leads us to the concept of logarithms.
Dialogue: 0,0:00:37.00,0:00:39.00,Default,,0000,0000,0000,,Well, what are logarithms?
Dialogue: 0,0:00:39.00,0:00:41.00,Default,,0000,0000,0000,,Let's take the base number - b - and raise it to a power, p,
Dialogue: 0,0:00:41.00,0:00:43.00,Default,,0000,0000,0000,,like 2 to the 3rd power
Dialogue: 0,0:00:43.00,0:00:46.00,Default,,0000,0000,0000,,and have it equal a number n.
Dialogue: 0,0:00:46.00,0:00:49.00,Default,,0000,0000,0000,,We get an exponential equation b raised to the p power equals n.
Dialogue: 0,0:00:49.00,0:00:52.00,Default,,0000,0000,0000,,In our example, that'd be 2 raised to the 3rd power equals 8.
Dialogue: 0,0:00:52.00,0:00:56.00,Default,,0000,0000,0000,,The exponent p is said to be the logarithm of the number n.
Dialogue: 0,0:00:56.00,0:01:02.00,Default,,0000,0000,0000,,Most of the time this would be written "log base b of a number equals p, the power."
Dialogue: 0,0:01:02.00,0:01:06.00,Default,,0000,0000,0000,,This is starting to sound a bit confusing with all the variables,
Dialogue: 0,0:01:06.00,0:01:08.00,Default,,0000,0000,0000,,so let's show this with an example.
Dialogue: 0,0:01:08.00,0:01:11.00,Default,,0000,0000,0000,,What is the value of log base 10 of 10 thousand?
Dialogue: 0,0:01:11.00,0:01:14.00,Default,,0000,0000,0000,,The same question could be asked using exponents.
Dialogue: 0,0:01:14.00,0:01:17.00,Default,,0000,0000,0000,,10 raised to what power is 10 thousand?
Dialogue: 0,0:01:17.00,0:01:20.00,Default,,0000,0000,0000,,Well, 10 to the 4th is 10 thousand. So, log base 10 of 10 thousand
Dialogue: 0,0:01:20.00,0:01:22.00,Default,,0000,0000,0000,,must equal 4.
Dialogue: 0,0:01:22.00,0:01:26.00,Default,,0000,0000,0000,,This example can also be completed very simply on a scientific calculator.
Dialogue: 0,0:01:26.00,0:01:29.00,Default,,0000,0000,0000,,Log base 10 is used so frequently in the sciences
Dialogue: 0,0:01:29.00,0:01:34.00,Default,,0000,0000,0000,,that it has the honor of having its own button on most calculators.
Dialogue: 0,0:01:34.00,0:01:37.00,Default,,0000,0000,0000,,If the calculator will figure out logs for me,
Dialogue: 0,0:01:37.00,0:01:39.00,Default,,0000,0000,0000,,why study them?
Dialogue: 0,0:01:39.00,0:01:43.00,Default,,0000,0000,0000,,Just a quick reminder, the log button only computes logarithms of base 10.
Dialogue: 0,0:01:43.00,0:01:47.00,Default,,0000,0000,0000,,What if you want to go into computer science and need to understand base 2?
Dialogue: 0,0:01:47.00,0:01:49.00,Default,,0000,0000,0000,,So what is log base 2 of 64?
Dialogue: 0,0:01:49.00,0:01:53.00,Default,,0000,0000,0000,,In other words, 2 raised to what power is 64?
Dialogue: 0,0:01:53.00,0:01:58.00,Default,,0000,0000,0000,,Well, use your fingers. 2, 4, 8, 16, 32, 64.
Dialogue: 0,0:01:58.00,0:02:03.00,Default,,0000,0000,0000,,So log base 2 of 64 must equal 6.
Dialogue: 0,0:02:03.00,0:02:05.00,Default,,0000,0000,0000,,So what does this have to do with my eyes turning red
Dialogue: 0,0:02:05.00,0:02:08.00,Default,,0000,0000,0000,,in some swimming pools and not others?
Dialogue: 0,0:02:08.00,0:02:12.00,Default,,0000,0000,0000,,Well, it leads us into an interesting use of logarithms in chemistry:
Dialogue: 0,0:02:12.00,0:02:15.00,Default,,0000,0000,0000,,finding the pH of water samples.
Dialogue: 0,0:02:15.00,0:02:17.00,Default,,0000,0000,0000,,pH tells us how acidic or basic a sample is,
Dialogue: 0,0:02:17.00,0:02:22.00,Default,,0000,0000,0000,,and can be calculated with the formula pH equals negative log base 10
Dialogue: 0,0:02:22.00,0:02:25.00,Default,,0000,0000,0000,,of the hydrogen ion concentration, or H plus.
Dialogue: 0,0:02:25.00,0:02:29.00,Default,,0000,0000,0000,,We can find the pH of water samples with hydrogen ion concentration of
Dialogue: 0,0:02:29.00,0:02:32.00,Default,,0000,0000,0000,,point 0-0-0-0-0-0-0-3-9-8
Dialogue: 0,0:02:32.00,0:02:37.00,Default,,0000,0000,0000,,and point 0-0-0-0-0-0-0-0-3-9-8
Dialogue: 0,0:02:37.00,0:02:40.00,Default,,0000,0000,0000,,quickly on a calculator. Punch:
Dialogue: 0,0:02:40.00,0:02:45.00,Default,,0000,0000,0000,,negative log of each of those numbers, and you'll see the pHs are 7.4 and 8.4.
Dialogue: 0,0:02:45.00,0:02:48.00,Default,,0000,0000,0000,,Since the tears in our eyes have a pH of about 7.4,
Dialogue: 0,0:02:48.00,0:02:54.00,Default,,0000,0000,0000,,the H plus concentration of .70398 will feel nice on your eyes.
Dialogue: 0,0:02:54.00,0:02:58.00,Default,,0000,0000,0000,,But the pH of 8.4 will make you feel itchy and red.
Dialogue: 0,0:02:58.00,0:03:02.00,Default,,0000,0000,0000,,It's easy to remember logarithms - log base b of some number n
Dialogue: 0,0:03:02.00,0:03:07.00,Default,,0000,0000,0000,,equals p - by repeating "the base raised to what power equals the number?"
Dialogue: 0,0:03:07.00,0:03:12.00,Default,,0000,0000,0000,,The base raised to what power equals the number? The base raised to what power equals the number?
Dialogue: 0,0:03:12.00,0:03:14.00,Default,,0000,0000,0000,,So now we know logarithms are very powerful
Dialogue: 0,0:03:14.00,0:03:17.00,Default,,0000,0000,0000,,when dealing with extremely small or large numbers.
Dialogue: 0,0:03:17.00,9:59:59.99,Default,,0000,0000,0000,,Logarithms can even be used instead of eyedrops after swimming.