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Math Help - SOlve the equation index

  1. #1
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    SOlve the equation index

    Solve the equation 2^{4-x} - 2^{3-x} = \frac{1}{8}
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  2. #2
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    Quote Originally Posted by mastermin346 View Post
    Solve the equation 2^{4-x} - 2^{3-x} = \frac{1}{8}
    Since 2^{4 - x} = 2 \cdot 2^{3 - x}, the equation simplifies to 2^{3-x} = \frac{1}{8}. Try solving it now.
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  3. #3
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    i get :

    2^{3-x} = \frac{1}{8}

    2^{3-x} = 2^{-3}

    3-x = -3

    x = 6

    then?
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  4. #4
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    Quote Originally Posted by mastermin346 View Post
    i get :

    2^{3-x} = \frac{1}{8}

    2^{3-x} = 2^{-3}

    3-x = -3

    x = 6

    then?
    Then you check to see whether or not it solves the original equation.
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  5. #5
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    \left(\frac{2^4}{2^x}\right) - \left(\frac{2^3}{2^x}\right) = \frac{1}{8}

    \frac{1}{2^x}\left(16 - 8 \right) = \frac{1}{8}

    \frac{8}{2^x} = \frac{1}{8}

    64 = 2^x

    2^6 = 2 ^x

    x = 6

    am i right?
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  6. #6
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    as said above by Mr F, plug x=6 in your question to check if it satisfies the equality.
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  7. #7
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    Quote Originally Posted by mastermin346 View Post
    \left(\frac{2^4}{2^x}\right) - \left(\frac{2^3}{2^x}\right) = \frac{1}{8}

    \frac{1}{2^x}\left(16 - 8 \right) = \frac{1}{8}

    \frac{8}{2^x} = \frac{1}{8}

    64 = 2^x

    2^6 = 2 ^x

    x = 6

    am i right?
    As I said before, substitute your answer into the given equation. Does it work? If it does work, then yes x = 6 is right. If it doesn't work then no x = 6 is not right.

    You do not need someone to check this answer ....
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