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Math Help - Logs and real variables.

  1. #1
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    Logs and real variables.

    Hello, Iam hoping to get some help with a question I have for an assignment ...

    Real variables x and y are related by the equation

    "ln(2+y) = 5ln(3 - x) - 2 sqrt x .....(sorry, I haven't as yet got the hang on LaTeX)

    Determine the range of values of x and y for which the expressions on each side of this equation are defined."

    I haven't really been able to make an attempt at a solution. I think I have to take the exp of each side, but I am not sure excatly what way I go about this, so if someone could give me some advice, that would be fantastic.

    Thanks in advance.

    Sean
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  2. #2
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    Since powers of e are always positive, the natural logarithm function \ln\, x is only defined for positive values of x. Similarly, since squares are always nonnegative, the function \sqrt{x} is only defined for nonnegative real numbers.

    For \ln\,(2 + y) to be defined, 2 + y must therefore be positive.

    For 5\,\ln\,(3 - x) - 2\sqrt{x} to be defined, both terms must have a value and thus be defined individually. Therefore, 3 - x must be positive, and x must be nonnegative.

    To view the LaTeX source code for any formula on this forum, you can click on it.
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  3. #3
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    Thanks

    I have it now. I thought it was more complicated than it was.

    Cheers

    Sean
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