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### The Difference Between Log and Natural Log

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Date: 8 Feb 1995 20:05:32 -0500
From: Anonymous
Subject: Logarithms

What is the difference between log and natural log?
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Date: 8 Feb 1995 22:29:17 -0500
From: Dr. Sydney
Subject: Re: Logarithms

Hello!

Suppose we have y = lnx; z = log t
where ln is log base e and log is log base 10.
Then these equations are equivalent to the following
statements:
e^y = x; 10^z = t

Sometimes it is easier to think of logs in these terms instead!
So, the difference is in the base -- ln has base e, log has base 10.

Hope this helps!  Write back if you have any more problems!

Sydney, "dr. math"
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Date: 8 Feb 1995 23:41:01 -0500
From: Elizabeth Weber
Subject: Re: Logarithms

Now, what is e?  Well, it's real name is Euler's number, and it's
equal to 2.71828182......

But why would we care enough about e to have a special kind of
logarithm for it?  Well, for some reason it's a number that pops
up all over the place (Especially when you learn calculus).  For
instance, if you draw the graph of 1/x, the area between this
graph and the x-axis between x=0 and x=1 is the natural log
of x.....but that's calculus.

But you don't have to be using calculus to run into e occasionally.
e shows up in statistics and in growth problems.  You've learned
about interest, right?  If you have a hundred dollars, and the
interest rate is 10%, you soon have \$110, and the next time
interest is figured out you're adding another 10% of \$110, so
you'll get \$121, and so on...  What happens when the interest
is being computed continuously (all the time)?  You might think
you'd soon have an infinite amount of money, but actually, you
have your initial deposit times e to the power of the interest rate
times the amount of time:

(interest rate x time)
(deposit) (e)

And e just naturally shows up again in growth problems, and in
some statistics problems too, which is why we bother giving the
natural log a special name.

Elizabeth, a math doctor
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Associated Topics:
High School Logs
High School Transcendental Numbers

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