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How to solve this non lenear equation

  1. May 11, 2009 #1
    \ln {v_0}=\ln{e^{\frac{-v_0}{100}}}^{100}\\
    the answer is [tex]v_0=56.7[/tex]
    how to find [tex]v_0[/tex]
  2. jcsd
  3. May 11, 2009 #2


    Staff: Mentor

    You can't solve this type of equation by algebraic means, but you can use approximation techniques to get an approximate solution, which v0 = 56.7 appears to be.
  4. May 11, 2009 #3

    Shooting Star

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    Homework Helper

    This is one way of doing it.


    Putting [itex]
    {\textstyle{{{\rm v}_{\rm 0} } \over {100}}} = x, x = e^{ - x} \Rightarrow x = 1 - x + x^2 /2,
    [/itex] retaining up to the second order term after expanding [itex]e^{-x}.[/itex]

    Now solve for x to get the approximate value. Justify why you are neglecting one value.
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