Talk:Lambert W function

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Comment
For instance, to solve the equation 2^t\,\! = 5 t\,\!
we divide by 2^t\,\! to get 1\,\! = \frac{5 t}{2^t}\,\!
convert to exponential 1\,\! = 5 t \, e^{-t \log 2}\,\!
divide by 5 \frac{1}{5}\,\! = t \, e^{-t \log 2}\,\!
multiply by -1 * log 2 \frac{- \, log 2}{5}\,\! = - \, t \, log 2 \, e^{-t \log 2}\,\!
replace -t \log 2\,\! with X\,\! \frac{- \, log 2}{5}\,\! = X \, e^X\,\!
Now application of the W function yields X \,\! = W \left ( \frac{- \, log 2}{5} \right ) \,\!
replace X\,\! with -t \log 2\,\! -t \log 2\,\! = W \left ( \frac{- \, log 2}{5} \right ) \,\!
Isolate t t \,\! = \frac{- \, W \left ( \frac{- \, log 2}{5} \right )}{log 2} \,\!


[edit] Request

Can we get an image of a fractal related to the Lambert W fun? If anyone has one (or can construct one), this article would benefit from its inclusion. (I know that fractals are not why Lambert W is important, and that Lambert W has more benefit as an equation implicitly defined by an elementary equation though it, itself is not an elementary equation, however a picture (of a fractal), and its ascetic beauty cultivate further interest in this most interesting function). -- LinuxDude 17:20, 8 January 2007 (UTC)

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