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Math Help - Simple algebra

  1. #1
    Member Altair's Avatar
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    Simple algebra

    Looks like simple algebra but can't do it.

    The numerical vale of the following forms come equal. But I can't convert the 1st form into 2nd :-

    1st. ln {\frac{(\sqrt{1+x^2} - 1)(\sqrt{1+y^2} - 1)}{|xy|}}

    2nd. -ln {\frac{(\sqrt{1+x^2} + 1)(\sqrt{1+y^2} + 1)}{|xy|}}

    Please show the steps.
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
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    Quote Originally Posted by Altair View Post
    Looks like simple algebra but can't do it.

    The numerical vale of the following forms come equal. But I can't convert the 1st form into 2nd :-

    1st. ln {\frac{(\sqrt{1+x^2} - 1)(\sqrt{1+y^2} - 1)}{|xy|}}

    2nd. -ln {\frac{(\sqrt{1+x^2} + 1)(\sqrt{1+y^2} + 1)}{|xy|}}

    Please show the steps.
    For this to be true, then:

    \frac{(\sqrt{1+x^2} - 1)(\sqrt{1+y^2} - 1)}{|xy|} = \left[\frac{|xy|}{(\sqrt{1+x^2} + 1)(\sqrt{1+y^2} + 1)}\right]

    (\sqrt{1+x^2} - 1)(\sqrt{1+y^2} - 1)(\sqrt{1+x^2} + 1)(\sqrt{1+y^2} + 1) = (xy)^2

    (1+x^2-1)(1+y^2-1) = (xy)^2

    (xy)^2 = (xy)^2

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  3. #3
    Member Altair's Avatar
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    I want the conversion from 1st form to the 2nd.Not its proof.
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  4. #4
    GAMMA Mathematics
    colby2152's Avatar
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    Quote Originally Posted by Altair View Post
    I want the conversion from 1st form to the 2nd.Not its proof.
    Showing the path from one form to another is a proof. It is unfortunate that my answer is not good enough for you.

    Why did I setup the first line of my problem like so?

    This comes from a log property: log(a^b)=b*log(a)
    In this case, b=-1 hence why the 2nd term in my 1st line is a reciprocal of what is being logged in your 2nd equation.
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