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Math Help - Algebra

  1. #1
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    Algebra

    Given that \frac{(144p^4)^{\frac{3}{2}}}{(216p^{-3})^\frac{-2}{3}}=2^x3^yp^z

    Find the values of x, y and z
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  2. #2
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    I'm not getting the question.

    There are 4 variables in 1 equation, and you want to find the values of 3 of them? There would be infinite solutions.
    So I'm assuming you want to rewrite the equation in the form x = ... y = ... and z = ... ?

    First, we can simplify the equation

    \dfrac{(144p^4)^{\frac{3}{2}}}{(216p^{-3})^\frac{-2}{3}}=2^x3^yp^z

    (144p^4)^\frac{3}{2} \times (216p^{-3})^\frac{2}{3}}=2^x3^yp^z

    1728p^6 \times 36p^{-2}=2^x3^yp^z

    62208p^4 =2^x3^yp^z

    Now can you use the rules of logarithms to rewrite them in the form x=... and so on?
    Or are you asking for something else?
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  3. #3
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    The questions wants me to find the value of x, y and z

    answer is x=8, y=5, z=4

    I have done wat u have done before i started this thread, couldnt find a way to change that number into powers of 2 and 3. Z was easily done problem lies in x and y for me...
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  4. #4
    Senior Member Educated's Avatar
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    That is a badly worded question.

    There are infinite solutions to what it is asking, for example:
    p=2, y=1, z=1, x= \frac{\log{165888}}{\log{2}} and this would still satisfy the question. This was just from me substituting random digits for 3 variables and solving for the fourth.
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  5. #5
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    Sorry the actual question should be:

    [QUOTE=Punch;562593]Given that \frac{(144p^4)^{\frac{3}{2}}}{(216p^{-3})^\frac{-2}{3}}=2^x3^yp^z

    Evaluate x,y and z
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  6. #6
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    You can write 144 and 216 as

    144 = 2^43^2 and 216 = 2^33^3

    Substitute in the given problem and simplify and compare the powers of 2, 3 and p.
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  7. #7
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    Quote Originally Posted by Educated View Post
    That is a badly worded question.
    Agree.
    You can even solve for p: p = (2^x 3^y / 62208)^[1 / (4-z)]
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  8. #8
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    Hi. thanks for your reply, can u show me the process of getting those numbers?
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  9. #9
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    Quote Originally Posted by Punch View Post
    Hi. thanks for your reply, can u show me the process of getting those numbers?
    What numbers?
    As it is, your problem is ambiguous; please submit the original in full.
    Or ask your teacher what the purpose is.
    Since your equation can be rearranged this way: 2^x 3^y / p^(4-z) = 62208,
    then we can set p=1 and z=3, so that we're dealing with 2^x 3^y = 62208
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