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Math Help - Solve algebra

  1. #1
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    Solve algebra

    Can anyone help me with this:

    3^(n-6) x y^(4n-8) = 1

    Find n and y.

    Thanks so much!

    There are three variables and I don't know how to solve it.
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  2. #2
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    Quote Originally Posted by ardnas
    Can anyone help me with this:

    3^(n-6) x y^(4n-8) = 1

    Find n and y.

    Thanks so much!

    There are three variables and I don't know how to solve it.
    I am sure that the "x" is not a variable here, that x is "times".

    Here is one way.

    3^(n-6) * y^(4n-8) = 1
    Divide both sides by 3^(n-6),
    y^(4n-8) = 1/ [3^(n-6)]
    y^(4n-8) = 3^[-(n-6)]
    y^(4n-8) = 3^(6-n) -----------***

    So, if (4n-8) = (6-n), then y=3.

    4n -8 = 6 -n
    4n +n = 6 +8
    5n = 14
    n = 14/5 = 2.8

    Therefore, n=2.8 and y=3. ---------answer.

    -----------------------------
    There could be infinitely many sets of answer, not only (n=2.8, y=3), but I won't investigate that anymore. I assumed you need at least one set of answers only.

    -------------------------
    Check,
    3^(n-6) * y^(4n-8) = 1
    3^(2.8 -6) * 3^(4*2.8 -8) =? 1
    3^(-3.2) * 3^(11.2 -8) =? 1
    3^(-3.2) * 3^(3.2) =? 1
    3^[(-3.2) +3.2] =? 1
    3^0 =? 1
    1 =? 1
    Yes, so, OK.
    Last edited by ticbol; February 10th 2006 at 07:50 PM. Reason: Let me check that.
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  3. #3
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    Oh I am sorry, the equation should read

    3^(n-6) * y(4n-8) = a
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  4. #4
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    Quote Originally Posted by ardnas
    Oh I am sorry, the equation should read

    3^(n-6) * y(4n-8) = a
    Zeez. Are you sure it is not equal to b instead?
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  5. #5
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    I am really sorry I mixed up the number and the letter.
    I've tried using log but it just gets worse, it becomes more and more complicated.
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by ardnas
    I am really sorry I mixed up the number and the letter.
    I've tried using log but it just gets worse, it becomes more and more complicated.
    If you could tell us what you expect a solution to look like that might
    help. You won't get an answer like y=7, n=2, a=3 from this, as a single
    equation will normally only give explicit numerical answers for one unknown.

    It would be usual to treat "a" as an unknown constant and solve for the
    other unknowns in terms of it, but here we still have two unknowns y and n,
    which define a curve in the y n plane.

    RonL
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