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Sonar Equation

  1. Dec 24, 2007 #1

    Trying to solve an equation about sonar range equation and can not end up with a feasible solution.

    The equation to be solved for x is as follows;

    10*log10(x) + a*x = b

    Any idea/suggestion/solution will help a lot.
  2. jcsd
  3. Dec 24, 2007 #2


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    Science Advisor

    You are not going to get any simple solution to that. You might be able to get a solution in terms of the "Lambert W function". It is defined as the inverse to the function xex.
  4. Dec 24, 2007 #3
    My first solution for the equation

    [tex] 10\log10(x)+ax = b[/tex] via Lambert W function was

    [tex] x = \frac{4.35}{a} * LambertW(\frac{a}{4.35}\exp(\frac{b}{4.35})) [/tex]

    I tested it again. It gives the correct results.

    Thanks alot.
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