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Math Help - simplifying logs

  1. #1
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    simplifying logs

    log7(x-sqrt(x2-21))+log7(x+sqrt(x2-21))

    i tried multiplying but i keep getting different answers
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  2. #2
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    Re: simplifying logs

    log_{7}(x-\sqrt{x^{2}-21})+log_{7}(x+\sqrt{x^{2}-21})

    log_{7}[(x-\sqrt{x^{2}-21})(x+\sqrt{x^{2}-21})]

    log_{7}(x^{2}-(x^{2}-21))

    log_{7}(21)
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  3. #3
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    Re: simplifying logs

    Quote Originally Posted by grillage View Post
    log_{7}(x-\sqrt{x^{2}-21})+log_{7}(x+\sqrt{x^{2}-21})

    log_{7}[(x-\sqrt{x^{2}-21})(x+\sqrt{x^{2}-21})]

    log_{7}(x^{2}-(x^{2}-21))

    log_{7}(21)
    Why is it not Log7(-21)?
    because the x2 cancles and you are left with -21?

    my aswer choices are
    1. log3 7
    2. log7 3
    3. 7 + log7 3
    4. 1 + log7 3
    5. 1 + log3 7
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  4. #4
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    Re: simplifying logs

    The 21 is inside the bracket so you have a double minus making a plus

    log_{7}(21)=log_{7}(7)+log_{7}(3)

    1+log_{7}(3)
    Thanks from chewydrop
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