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Topic: [ap-stat] Log vs ln
Replies: 1   Last Post: Nov 14, 2010 12:01 AM

 david.kit.friedman@gmail.com Posts: 101 From: Youngsville, North Carolina Registered: 5/14/09
Re: [ap-stat] Log vs ln
Posted: Nov 14, 2010 12:01 AM

On 11/13/2010 3:58 PM, David Bock wrote:
>
> On Nov 13, 2010, at 11:42 AM, Cindy Hasselbring wrote:
>

>> My AP class is working on linear transformations.When working with
>>
>> exponential and power models, is there a rule of thumb for when to use
>>
>> common log and when to use natural log for the transformation?
>>

>
> It does not matter. A logarithm is a logarithm is a logarithm. Log and
> ln differ by a constant factor, since log x = lnx/ln10. Kids may work
> with whichever they like -- but note that they could be given an
> equation that uses either, so be sure they're ok with both.
>
> -- Dave
>

If one were to make an example data set with a
column for x, a column for y, a column for ln(y) (the
natural log of y) and a column for log(y) (the common log of y),
one would see that the numbers in the column for log(y)
are just the numbers in the ln(y) column multiplied
by a constant factor.

This is just because log(y) = ln(y) / ln(10)

If one were then to compare the regression lines for
ln(y) vs. x and log(y) vs. x it would be seen that the
coefficients differ by the factor 1/ln(10).

This is because multiplying all the y-values by
the same number changes the slope and the intercept values
by that same number.

In many ways it is similar to whether y in measured in
yards or meters.

Also, just a quick note that some text or software will use the notation
"log" to mean natural logarithm

http://www.wolframalpha.com/input/?i=log(2.718)+
<http://www.wolframalpha.com/input/?i=log%282.718%29+>

While a TI-84 calculator will say log(2.718) is about 0.434

See for example:

http://mathworld.wolfram.com/Logarithm.html

"Note that while logarithm base 10 is denoted log x in this work,
on calculators, and in elementary algebra and calculus textbooks,
mathematicians and advanced mathematics texts uniformly use
the notation log x to mean ln x...."

David

P.S.

Sampling of different software and it's definition of "log"

Excel -- "log" means common log:
Google -- "log" mean common log:
R -- "log" means natural log: http://www.r-project.org/
Maxima -- "log" means natural log: http://maxima.sourceforge.net/

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