# Logarithms, Explained – Steve Kelly

How does the difference between point 0000000398 and point 00000000398 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 10,000? The same question could be asked

using exponents: “10 raised to what power is 10,000?” Well, 10 to the 4th is 10,000. So, log base 10 of 10,000 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 0000000398 and point 00000000398 quickly on a calculator. Punch: negative log

of each of those numbers, and you’ll see the pH’s are 7.4 and 8.4. Since the tears in our eyes

have a pH of about 7.4, the H plus concentration of .0000000398 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?” 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.

"a way of dealing with smaaaall numbers, or in some case extremely laaaarge numbers. this leads us to the concept of LOOOOgarithms."

Logarithms were a base for calculations during my dad's college time. They didn't had scientific calculators as we have so every big calculations must be converted to log.

What I still don’t understand is why bother with logs at all? They seem to be just a flipped around version of exponents. They don’t bring any new information to the table, they just move around the variables when dealing with exponents. Am I missing something?

If Base^power=number why do we have to rearrange the whole equation to make it look so convoluted?

I managed to learn what it takes school a month to teach in 3 and a half minutes.

is it just me or does he sound like Ross from Friends?? or am i just crazy??

Does this guy have asthma?

Thank you! Excellent explanation!

Im not good at math but can't you just use a root instead?

i like his way of saying zero

Ok work it out Log base 2 of 7.

l o o a g a r i t h moh my gosh!! i am intelling than an average guy on a street now!!

rouzy rouzy rouzy rouzy rouzy rouzy rouzy lol

This was not a very good explanation

Now LoLgorithm please

The narrating dude talks weird…

Very nice animation and very good explanation

This guys voice is painful to listen to

thankyou

This guy say log so hypnotically!

Anyone else want to punch this guy in the face?

godfuckinbless m8

"The log key on your calculator only does log_10."

log_b(p) = ln(p) / ln(b)

LOOOOOOOOOGRITHMS

excellent video — thnks a ton

Simple and easy💕

I would love more computer science examples of the use of logarithms. Like in Big O notation!

Very simple and awesome explanation!

Algorithm

logArithm

WhatHurray for computer science

Must say a Thankyou

1:40 You can do another base!

Example: log_2(π)= log(π)/log(2) or ln(π)/ln(2)* = 1.651496129

log_17(262,144) = log(262,144)/log(17) or ln(262,144)/ln(2) = 4.403709758

good info

But… Somebody didn't understand this easy topic?

This is the basics. I do not think that someone had difficulties with this.

Awesome

Im a student and I can easily say that this video CANNOT get any bettet than this….while there are videos with 16-20 min and does not make us understand one bit, this does in 3 min….a succes according to me…im satisfied 😉😉😉

When he says zero it also sounds like he says Rosie

First Define what is Log

Red what??

LAWGRYTHYMS !!

This did nothing to explain what they are. Just gave a definition using exponents. Why do we need log when we have exponents. It seems like the exact same idea just a different definition of the same idea.

Lol. I love when you look away from the screen but look back again, it look so complicated but if you watch the video it's explained perfectly well 🙂

Lolsrithm

This video made logarithmic easy

This was amazingly explained

Okay. Check this video out https://youtu.be/96UdV5SeDD4

asm explanation man😃😃😃😃😃😃

what if the c=10M?!

Eddie Woo explained it way better than this

So well

The Base raise to what power is equal the number ?

The Base raise to what power is equal the number ?

The Base raise to what power is equal the number ?

The Base raise to what power is equal the number ?

The Bash raise to watt pawer equal the bumber ?

The Bash raise to watt pawer equal the bumber ?

The Bash raise to watt pawer equal the bumber ?

The Bash raise to watt pawer equal the bumber ?

I love this guy's voice lol maths can be boring so im glad i can watch with his voice narrates this

Nice 😍😍😍

Watch this

https://youtu.be/8WYvV5pbFLQ

Am I the only one who expected that "Satisfying" voice in this video?

Lmfao at 1:09…"What is the value of Log base tena TEN THOUSAND!?!" take it easy buddy, your slurring your math.

Wow logarithm and Ph that’s awesome!!! Then maybe scientists who are working in NASA or biologists will Logarithm right? Awesome!!!!

Fooooor merci

Funny, my math teacher couldn't answer this simpel question.

Looking at this video I can see that Ted Ed has grown so much, wow.

I still don't get it

Thank you so so much

are you perhaps related to THE NED KELLY?

Funny and useful

OMG this was so cool 😂

Love you bro what an awesome exlpaination😣👏👏👏👏👏👏🤟

Rosie Rosie Rosie Rosie Rosie Rosie Rosie Rosie Rosie Rosie….

You sound like being chased by a dog. Sorry.

https://www.desmos.com/calculator/sbrleia005 link to ph lab

So you're saying is its the same as roots, right?

nice

oml this is so helpful! :0

I'm 30yo now and this reminded me how terrible I was with logs in school. Finally I understood. Base, Power, Number.

Log has 2 buttons on my calculator

Great information, but the guy narrating this is trying way too hard to be interesting and keep your attention, and it’s really distracting.

TED-ED a day keeps fear away for a day.

veryyyyy helpful wow

veryyyyy helpful wow

Rupa madarchod hain.

Rupa madarchod hain.

LOOOOOGarthms

I was holding a cup of milk in one hand and a croissant in the other when the narrator said, "c'mon, use your fingers" (1:54). I started counting with him and dropped my croissant first, then I dropped my cup of milk and it broke and got all over the place.

why you allways say poin some number and exclude zero numbers dont begin with dots

I wish my teacher was this enthusiastic…

You know what's funny

I had this same question log 10 10,000= on one of my map test questions

(^m^;) 😛 (^J^)

Steve Kelly is awesome!

that first animation is too fast.

The logarithms are more brilliant than I thought.

Omg thank you!!!

I hear rowsy rowsy instead of zero who else ??

Logarithms often cause me to get red eyes.

Oh man! The way this educator explain his lesson with his unique way of talking… Recommended educator

Would of been better example if shown correct way to enter keystrokes on a calculator

It did not explain how log can simplify by doing what exactly. In the video you still are trying to find the exponent.

The way I remember the general for is;

Log10(1000)=3

From here its clear to see base 10^3=1000

I'd like to see more of these from this guy but sometimes he speaks too quickly I think.

A-ha!

Just great

THIS changed my life …. god's work #blessup

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