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VCE Stuff => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematics => Topic started by: Furbob on September 04, 2010, 12:30:33 pm

Title: What exactly is a "log"?
Post by: Furbob on September 04, 2010, 12:30:33 pm: 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?"
Title: Re: What exactly is a "log"?
Post by: Hutchoo on September 04, 2010, 01:03:49 pm: http://en.wikipedia.org/wiki/Logarithm

Read that, make a summery.
Title: Re: What exactly is a "log"?
Post by: TrueTears on September 04, 2010, 08:05:23 pm: Quote from: Furbob on September 04, 2010, 12:30:33 pm
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.
Title: Re: What exactly is a "log"?
Post by: Mao on September 06, 2010, 09:09:09 pm: 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, $\log_{10}(20)$ 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.
Title: Re: What exactly is a "log"?
Post by: jimmy999 on September 12, 2010, 07:12:38 pm: 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
Title: Re: What exactly is a "log"?
Post by: TrueTears on September 12, 2010, 07:17:22 pm: Quote from: jimmy999 on September 12, 2010, 07:12:38 pm
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:

Quote
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, $e$ is a definition, namely the value of this limit: $e = \lim_{n\to\infty} \left( 1 + \frac{1}{n} \right)^n$

In words, this translates to:

Quote
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.
Title: Re: What exactly is a "log"?
Post by: Ahmad on September 12, 2010, 09:12:14 pm: An interesting blog post that's somewhat related to this: http://gowers.wordpress.com/2007/09/13/how-should-logarithms-be-taught/