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Q&A #3572

Teachers' Lounge Discussion: Logarithmic functions

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From: Marielouise 
To: Teacher2Teacher Public Discussion
Date: 2000071311:15:16
Subject: Re: Logarithms

When you are talking with your student about exponents, have the
student pay attention to the base.  For example:  10^0 = 1, 10^1 = 10,
10^2 = 100, etc.
You notice that as the exponents increase by one that the answer
increases by a factor of ten.  If the example was:  3^0 = 1, 3^1 = 3,
3^2 = 9, etc.  In this case as the exponent increases by one the
answer is tripled from the previous one.  The point that I am trying
to make is that you are taking about not only the exponent but also
the base.

When you deal with logarithms, it is important to determine the value
of the base.   In "real life"  the base is either 10 or "e" for most
problems. However, in learning logarithms all integer bases are
generally used, in particular a base of 2 or three.

I taught with a woman who devised the following sentence for students
to learn:

a B(ase) raised to an E(xponent) is a N(umber)  if and only if the
log to the B(ase) of the N(umber) is the E(ponent).

B^E = N  if and only if log (to the Base) N = E.

She used capital letters so that the E stood for exponent and was not
be later confused with "e" the natural base.

If you use the approach above you will find that your problem:

log (x - 1) = 1 can be written as 10^1 = (x - 1)   By solving this
equation then x = 11.   It might help your students in the beginning
to write the base 10 with the common log.  Otherwise they frequently
forget that the base is 10.

You might also like to look over various problems listed on the Ask
Dr. Math site:

http://forum.swarthmore.edu/dr.math/tocs/logarithm.high.html

-Marielouise, for the Teacher2Teacher service


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