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Math Help - exponentials....i need help

  1. #1
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    exponentials....i need help

    I have two problems I am stuck on. I missed lecture and need help with both
    1. 256^x=4

    2. 1/9x=6561

    Thanks to anyone who can help me. Leilani
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  2. #2
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    Quote Originally Posted by leilani View Post
    I have two problems I am stuck on. I missed lecture and need help with both
    1. 256^x=4

    2. 1/9x=6561

    Thanks to anyone who can help me. Leilani
    1. Take the log of both sides (you can pick any base you like)

    You can use the rule log_b(a^k) = k \times log_b(a) ( b >0 , \neq 1) to bring x to the front and remove it as a power:

    As 256 = 2^8 and 4 = 2^2 we can write the equation as 2^{8x} = 2^2

    Spoiler:
    Take logs of both sides (I will use base e):

    8x \times ln(2) = 2ln(2)

    x = \frac{1}{4}

    (note that using base 2 in your logarithm will get log_2(2) = 1 so they get cancelled a step earlier)


    2. Do you mean \frac{1}{9}x or \frac{1}{9x} ?
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  3. #3
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    Quote Originally Posted by leilani View Post
    I have two problems I am stuck on. I missed lecture and need help with both
    1. 256^x=4

    2. 1/9x=6561

    Thanks to anyone who can help me. Leilani
    Hi leilani,

    2^8=256


    (1) 256^x=4

    2^{8x}=2^2

    8x=2

    x=\frac{1}{4}


    (2) Did you mean to write this: \left(\frac{1}{9}\right)^x=6561? I can't see your picture for some reason.


    If so, know that 3^8=6561 and \frac{1}{9}=\left(\frac{1}{3}\right)^2=3^{-2}


    Then,


    \left(\frac{1}{3}\right)^{2x}=3^8


    3^{-2x}=3^8


    -2x=8


    x=-4
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  4. #4
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    (1/9)x=6561

    It doesn't have the x as an exponent just as a multiplier
    Last edited by mr fantastic; April 23rd 2009 at 03:14 PM. Reason: Merged posts
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  5. #5
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    Quote Originally Posted by leilani View Post
    It doesn't have the x as an exponent just as a multiplier
    Like this \frac{1}{9}x=6561??

    This one is easier than the other one, then. Just multiply both sides by 9.
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  6. #6
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    Thanks, I got it. I set it up just like the other one. I think there was a mistake how they wrote the problem. When I worked it out just like the other one I got the right answer. Thanks very much! Leilani
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  7. #7
    A riddle wrapped in an enigma
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    Quote Originally Posted by leilani View Post
    Thanks, I got it. I set it up just like the other one. I think there was a mistake how they wrote the problem. When I worked it out just like the other one I got the right answer. Thanks very much! Leilani

    What was the right answer since we don't know how it was meant to be written in the first place?? Just for yuks.
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  8. #8
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    Quote Originally Posted by masters View Post
    What was the right answer since we don't know how it was meant to be written in the first place?? Just for yuks.
    X=-4
    Thanks for the help
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