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Thread: High school math analysis problem (log A)/A = C, solve for A

  1. #1 High school math analysis problem (log A)/A = C, solve for A 
    Forum Freshman GreatBigBore's Avatar
    Join Date
    Feb 2010
    That is, if I'm going about it right. Trying to help my kid with math and totally stumped. Original problem is like this:

    f(x) = 0.5x
    A * f(x) = f(x + A)
    Solve for A.

    I played around for a while and kept coming back to

    (log A) / A = log 0.5

    But I don't know where to go from there. The answer is given, but I couldn't figure out how to get there. Help!

    The most exciting phrase to hear in science is not “Eureka” but “That’s funny...” -- Isaac Asimov
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  3. #2  
    Bassaricyon neblina Olinguito's Avatar
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    Aug 2013
    Greater London, England, UK
    That’s the best you can do if you’re using only logarithms. There is no way to write explicitly as a combination of elementary functions of .

    However you can try the Lambert W function: this is not strictly speaking a function but a multivalued relation defined as iff .


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  4. #3  
    Forum Freshman
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    Jan 2013
    If they allow it, you could also plot the two curves and find at what value of A they intersect:

    solve ln(x)/x = ln(0.5) - Wolfram|Alpha
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