What is the logarithm

A logarithm is a power in which an amount should raised to essentially to get any additional digit. For instance, the base ten logarithm of 100 is 2 since ten to the power of two is 100.

The logarithm of a number is the power to which a 'base' must be raised

in order to get that number.

- - If the base is 10, then the logarithm is called the "common" logarithm.

The common logarithm of 100 is 2, because 10² = 100.

- - If the base is 'e', then the logarithm is called the "natural" logarithm.

The natural logarithm of 54.598 is 4 (rounded), because e⁴ = 54.598.

As you might have guessed, ' e ' is the number that's called "the base of

natural logarithms". Like 'pi', it can never be written exactly with digits.

It starts out 2.7 1828 1828 4590 45 ... and it keeps going forever.

You're probably wondering where ' e ' comes from, and all I can tell you

is that it pops up in millions of places in math and science.

Here's one example: Let's say you hate school so much that you really totally

don't want to be there. The closer you get to school in the morning, the slower

you walk. Every hour, you see how far you are from school, and you walk half

ofthat distance in the next hour. OK? You keep slowing down. Each hour, you

only walk half as far as you walked in the previous hour.

If you start out at 12:00, then as you go along, your distance from school

at any time is

(the total distance) times ' e ' raised to the power of - (0.693 x the time)

If the speed of something depends on how far it still needs to go, then the

speed, the acceleration, and the distance it covers all have ' e ' in them.