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Math Help - Solving the Unknown for Indices

  1. #1
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    Solving the Unknown for Indices

    Solve for 'x':

    3^2x - 8.3^x - 9 = 0
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  2. #2
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    Quote Originally Posted by Ogsta101 View Post
    Solve for 'x':

    3^2x - 8.3^x - 9 = 0
    3^{2x} - 8 \times 3^x - 9 = 0 \Rightarrow (3^x)^2 - 8 (3^x) - 9 = 0 \Rightarrow w^2 - 8w - 9 = 0 where w = 3^x.

    After a bit more working:

    Therefore 3^x = 9 = 3^2 or 3^x = -1.

    One of these has no real solutions. The other has one real solution.

    Therefore x = ......
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    3^{2x} - 8 \times 3^x - 9 = 0 \Rightarrow (3^x)^2 - 8 (3^x) - 9 = 0 \Rightarrow w^2 - 8w - 9 = 0 where w = 3^x.

    After a bit more working:

    Therefore 3^x = 9 = 3^2 or 3^x = -1.

    One of these has no real solutions. The other has one real solution.

    Therefore x = ......
    Does x = 3???

    I'm not completely sure because when I sub 3 back into the original question, it doesnt equal 0. So now I'm a little confused. But i do understand all the working...
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  4. #4
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    Quote Originally Posted by Ogsta101 View Post
    Does x = 3???

    I'm not completely sure because when I sub 3 back into the original question, it doesnt equal 0. So now I'm a little confused. But i do understand all the working...
    3^x = 3^2. The bases are the same. What does x have to equal to make the indices the same?? Hint: NOT 3!!
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    3^x = 3^2. The bases are the same. What does x have to equal to make the indices the same?? Hint: NOT 3!!
    Ugh - I did totally the wrong thing! Man I'm dumb. Ok I totally get it now!!!

    Thanx sooooooooooo MUCH!!!

    (x = 2 yeah?)
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  6. #6
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    Quote Originally Posted by Ogsta101 View Post
    Ugh - I did totally the wrong thing! Man I'm dumb. Ok I totally get it now!!!

    Thanx sooooooooooo MUCH!!!

    (x = 2 yeah?)
    Yeah!
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  7. #7
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    how 2 solve: 4^x=32
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  8. #8
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    4^x = (2^2)^x

    Knowing that
    32 = 2^5
    Thus

    2^{2x} = 2^5

    Hence

    2x = 5

    x = 5/2
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    Try to start new threads for new problems.Its better!
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