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"ln" is the symbol for "natural logarithm". The base is the number called ' e '. It's an

irrational number, so it can't ever be written down exactly. The beginning of it is

2.7 1828 1828 4590 45

(There's no reason for the spaces. That's just the method I use to remember it.)

' e ' is a very interesting number that seems to pop up almost everywhere in science,

math, and engineering.

' e ' always comes up in connection with any process where the speed of the

process depends on how far it has left to go. For example ... how fast does a

hot cup of coffee cool ? That depends on the temperature of the air around the

cup. The closer the coffee gets to the temperature of the surrounding air, the

slower it cools, and if you graph the temperature of the coffee against time,

the graph has the shape of the function

Temperature = e(time it's been cooling so far)

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Q: What is the logarithmic base of ln 12 equals 2.4849?
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