Teacher2Teacher 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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