The King of Numberland (Or, the Genesis of Logarithms)

[Trieste]

For TehFerret:

Once, long ago, there was the Land of Numbers. All the numbers lived here and they were happy...

... mostly. Except for the exponents.

For a long time, the exponents were treated like second-class citizens of numberland. They couldn't go anywhere without their base numbers, and they were never allowed to get quite as big as their bases. This made them so angry that they eventually started a revolution. They rabbleroused and robblehoused and eventually ended up at the door of the King of Numberland himself.

"We're forced to live as slaves!" the Head Exponent cried.

"YEAH!" chimed the other exponents.

"We can't live like this!" the Head Exponent declared.

"YEAH!" cried the other exponents.

"WE DEMAND A CHANGE!" proclaimed the Head Exponent.

"YEAH, YEAH!" chorused the other exponents.

The King of Numberland could see that his kingdom was in peril. He needed to do something. He called the base numbers in, and told them, "I'm sorry, but you're going to have to switch places with the exponents." The base numbers weren't happy with this, but what could they do?

"Hey, wait a minute," interjected the Head Exponent. "We've spent all this time riding on the shoulder of our bases. We deserve a little more than to switch places."

Beside himself, the King cried, "Well, what do you want?"

"We want to step on them!" the exponents cried! And the King, in the interest of preserving the peace in Numberland, agreed. Now, the base numbers REALLY weren't happy with this, but they didn't dare disobey the King.

And so the base numbers are forced to spend their days not only smaller than the exponents, but also being tread upon by them, with the help of Logarithm, the Great Mediator.

log_aB is the same as a^B

We usually work in base-10, so the LOG button on a calculator actually stands for log₁₀.

And because we use log_e so much, it's shortened into ln. That's all ln is - log_e.



This story was told to me by my pre-calc professor, and has seriously helped me with dealing with logs in calc. So I'm sharing it in the hopes that it helps someone else as well. :)

[DarklingAlice]

Thank you so much, Trieste. That is an excellent story. And quite helpful too as I am being forced to teach myself calculus all over again.

[Trieste]

You're welcome, I'm glad it helps! I just noticed and corrected a mistake, though: the LOG button actually stands for log₁₀, not log¹⁰... hit the wrong button.

[Satnslillgrl]

*Giggle*

That reminds me of the Soh-Cah-Toa story for remembering sine,cosine, and tangent.

[Trieste]

Sohcahtoa always reminded me of some ancient Mayan chant or some such. Can see the crowd below the huge pyramid chanting "SOHcahtoa, SOHcahtoa" as some beautiful young girl is brought up to the altar...

[Oniya]

Sohcahtoa always reminded me of some ancient Mayan chant or some such. Can see the crowd below the huge pyramid chanting "SOHcahtoa, SOHcahtoa" as some beautiful young girl is brought up to the altar...

That's how they managed to get all the angles in the pyramids to work out, didn't you know that?  ;D

[Satnslillgrl]

My high school Pre-Calc teacher told us a story...

There was once a young Native American girl who belonged to a small tribe. Everyone had their cool Native American names, like Running Bear and Sings To Squirrels (Yes, those were the actual examples she gave). Everyone except this girl. She didn't do anything special enough to earn a name.

So one day she was very sad about not having a name and decided to take a stroll through the woods. As she was walking, she stubbed her big toe on a rock. Limping in pain, she made her way over to a small pond that was nearby. She stuck her foot in and sat there, letting the cool water soothe her toe. 

A few moments later the tribe Chieftain rode by with a few of the hunters. He saw her looking very sad and asked her what was wrong. She told him that she was sad because she didn't have a name. The Chief pondered this for a moment. He looked at her, then down at her foot in the water, and then back up at her.

"I've got it! Your new name is Soh Cah Toa! (Get it, Soaking her toe *nerd giggle*)

And then that's it. Sine=Opposite over Hypotenuse, Cosine=Adjacent over Hypotenuse, and Tangent=Opposite over Adjacent. ^_^