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Mathematics
Ivy Herman
30 October, 20:00
What is the logarithm
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String Bean
30 October, 20:15
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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.
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Will Burton
30 October, 21:29
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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.
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