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### 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
```
Associated Topics:
High School Logs

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