Logarithms

Date: Wed, 2 Nov 94 14:57:48 EST
From: "Terry Strohecker"
Subject: Logarithms

Can you explain exactly what a logarithm is?  Thanks, I love this 
Dr. Math resource, I can see it's going to be very helpful.

Terry
stroheck@student.msu.edu

From: Dr. Ethan
Subject: Re: Logarithms
Date: Wed, 2 Nov 1994 15:35:50 -0500 (EST)

Terry,
        I'm not sure how in depth you want me to go.  If this is too basic,
write back for more.
        I think the easiest way to think about a logarithm is to think
"A logarithm is an exponent."    Or another way to say this is: y is a
logarithm if it solves an equation of the form

     a = b ^y  (That means a equals b to the y power)

An applied way to understand a logarithm is as the inverse of a growth 
curve.

Let's say you have a growth curve 

     (Population) = (growthfactor) ^(time)

This equation takes time and gives you the population at that time.  

If you wanted to know when the population is a certain size that equation
would be

     Log base (growthfactor) of (population) = time

That equation didn't come out too well; I hope you can figure that out.

If you want information about calculating with logarithms or these ideas
haven't helped your intuition, then write back and maybe someone else 
will have more things to say.

                Ethan Doctor on Call