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Math Help - how to emdas in logatirthm?

  1. #1
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    how to emdas in logatirthm?

    can somebody show me the proper step to solve for x

    50/(1 + e^-x) = 4

    first would be multiply denominator to 4,, .

    correct answer is somewhere at -2.44

    thanks
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  2. #2
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    You can do this: 50e^x  = 4e^x  + 4\; \Rightarrow \;46e^x  = 4\; \Rightarrow \;e^x  = \frac{2}{{23}}
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  3. #3
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    Quote Originally Posted by aeroflix View Post
    can somebody show me the proper step to solve for x

    50/(1 + e^-x) = 4

    first would be multiply denominator to 4,, .

    correct answer is somewhere at -2.44

    thanks
    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.
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