Logarithms

Date: 12/2/95 at 11:57:31
From: Anonymous
Subject: What are logarithems?

Dr. Math, 

    What is a logarithm?  If you could please let me know that would be 
great.

Date: 12/4/95 at 0:40:38
From: Doctor Ken
Subject: Re: What are logarithems?

Hello!

Logarithms are really neat!  Here's how they work.  You know that 3^2 = 
9, right (3^2 means three squared)?  Well, here's another way you can 
write that:

Log  9 = 2
   3

What that's supposed to look like is a "Log" with a subscript of 3.  The 
way you say that equation is "the log to the base 3 of 9 is 2."  The way 
you think about it is this: the log to the base x of y is the number you 
can raise x to to get y.  The log is the _exponent_.  That's how I 
remembered logs the first time I saw them: I just kept repeating "the 
log is the exponent, the log is the exponent, ..."  What I mean by that 
is that the log of some number is the exponent you have to raise the 
base to to get that number.

So let's do another example: What's the log to the base 5 of 625?  In 
other words, find the value of:

Log  625.
   5

Well, since 5^4 = 625, the log (to the base 5) of 625 is 4.

What's the log to the base 2 of 1024?

Here are a couple of rules that you can use when you're dealing with 
logs:

Log  (ab) = Log  a  +  Log  b
   x           x          x

Log (a^b) = b Log  a
   x             x

Enjoy!

-Doctor Ken,  The Geometry Forum