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AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Sunday, September 25, 2005

Blogging Logs and Exponents

One of the hardest things that I have found in this unit is logs, more specifically when you have a log in the exponent.

x^(ln x) = e^100

When you solve a power where there is a log in the exponent, if the base of the log in the exponent is the same as the base of the power itself, then the solution is easy. But when you don't know the base, then it's not as easy.

x^ln x = e^100
ln (x^ln x) = ln(e^100)
(ln x)^2 = 100
(ln x)^2 -100 = 0
(ln x -10)(ln x +10) = 0
ln x = +/-10
x = e^-10 x = e^10

This is an example of one of the problems we in class but it helped me learn how to deal with solving equations with logs and exponents better. I found this to be tough at first, but once we started working on it in class, it got easier and now I finally understand it. My moment of clarity came when Mr. K showed us a less complex example using base 2, seeing something you're so used to just got me over the hump, it feels good to get over the hump. An exponent is a log!

(this is my blog for the unit)

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  • At 9:37 PM CDT, Blogger Mr. Kuropatwa said…

    Well done Steve. Just one comment. The second line you wrote:

    ln (x^ln x) = ln(e^100)

    the bracket on the left hand side is misplaced. It should be written as:

    (ln x)^ln x = ln(e^100)

    then the rest follows. ;-)


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