You can do this:

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- Sep 13th 2010, 02:58 AM #1

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- Sep 13th 2010, 03:07 AM #2

- Sep 13th 2010, 03:57 AM #3

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Having first multiplied both sides by the denominator you have 50= 4(1+ e^{-x})= 4+ 4e^{-x} where I have used the "distributive law" to separate the term involving x from the constant term on the right. Now subtract 4 from both sides: 46= 4e^{-x}. Divide both sides by 4: 46/4= 23/2= e^{-x}. To get rid of the exponential now, do the "opposite"- take the natural logarithm of both sides: ln(23/2)= -x. Finally, multiply by -1.

Plato does it in a completely different way, first multiplying both numerator and denominator of the fraction on the left by e^x.