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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
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    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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    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  
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    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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