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Math Help - Logarithmic equation with parameter, please help

  1. #1
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    Logarithmic equation with parameter, please help

    I need to find all values of the real parameter "a" for which the equation \left| {a - \log x} \right| + \left| {a + \log x} \right| = 2 has two solutions. Find the solutions.
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  2. #2
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    Re: Logarithmic equation with parameter, please help

    Hey shervlad.

    Have you tried expanding out the absolute value to take care of all possible combinations?

    Hint: a - log(x) + a + log(x) = 2 for a - log(x) > 0 and a + log(x) > 0 is 1 equation. Can you expand the rest and find the two common solutions?
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  3. #3
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    Re: Logarithmic equation with parameter, please help

    yeah...but that's a dead-end way. What I did was I sqared the equation and so I got rid of one module, and it is much easier to work with only one module than with two, especially having to variables...
    If you are interested in the solution:
    Last edited by shervlad; January 10th 2013 at 10:36 PM.
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  4. #4
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    Re: Logarithmic equation with parameter, please help

    You might have to re-do it since the post says your equation is too long.
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