What exactly is a "log"?

[Furbob]

As the title says - what exactly is the definition of a log?

This popped up in my head from yesterday when my friend who does GMS asked what it was when she saw my work
but I couldn't really explain it to her so I just said "I dont know...it's pi's awkward cousin perhaps?"

[Hutchoo]

http://en.wikipedia.org/wiki/Logarithm

Read that, make a summery.

[TrueTears]

As the title says - what exactly is the definition of a log?

This popped up in my head from yesterday when my friend who does GMS asked what it was when she saw my work
but I couldn't really explain it to her so I just said "I dont know...it's pi's awkward cousin perhaps?"

The natural log is defined to be the inverse of the natural exponential.

[Mao]

Read this: http://vcenotes.com/forum/index.php/topic,4899.0.html

there's not too much explaining there, but there are a lot of examples.

But in a nutshell, is the question "10 to the power of what gives me 20?", apply that to a more general sense involving variables and you will get a slightly better idea.

[jimmy999]

First read this http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/
And then read this http://betterexplained.com/articles/demystifying-the-natural-logarithm-ln/

Gives a beautiful explanation about to what the exponential and logarithm really is. Also that site has a wonderful explanation for what complex numbers really are. I highly recommend this site to anyone interested in maths

[TrueTears]

First read this http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/
And then read this http://betterexplained.com/articles/demystifying-the-natural-logarithm-ln/

Gives a beautiful explanation about to what the exponential and logarithm really is. Also that site has a wonderful explanation for what complex numbers really are. I highly recommend this site to anyone interested in maths

From the first site it says:

e is the base rate of growth shared by all continually growing processes.  e lets you take a simple growth rate (where all change happens at the end of the year) and find the impact of compound, continuous growth, where every nanosecond (or faster) you are growing just a little bit.

I actually disagree with this, from a mathematician's point of view, is a definition, namely the value of this limit:

In words, this translates to:

The mathematical constant e is the unique real number such that the value of the derivative (slope of the tangent line) of the function f(x) = e^x at the point x = 0 is equal to 1.

[Ahmad]

An interesting blog post that's somewhat related to this: http://gowers.wordpress.com/2007/09/13/how-should-logarithms-be-taught/