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Math Help - Logarithms (^^,)

  1. #1
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    Question Logarithms (^^,)



    Hiii

    could someone help me ?!

    I have this problem and I solved it but I'm not sure if my answer is correct

    so I just want you to tell me if it's correct or not

    and if it wasn't correct .. maybe you can help me find the correct answer


    well .. ok

    log { base 4 } of x = 25 log { base x } of 4

    log { base 4 } of x = 25/[log { base 4 } of x]

    log { base 4 } of x - 25/[log { base 4 } of x] = 0

    let' say that K = log { base 4 } of x

    K - 25/K = 0

    (K)K - (K)25/K = (K)0

    (K^2) - 25 = 0

    K^2 = 25

    K = 5

    log { base 4 } of x = 5

    x = 4^5

    x = 1024


    is my answer correct ?!
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  2. #2
    MHF Contributor red_dog's Avatar
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    You missed a solution!
    (\log_4x)^2=25\Rightarrow \log_4x=\pm 5.
    If \log_4x=5\Rightarrow x=4^5=1024.
    If \log_4x=-5\Rightarrow x=4^{-5}=\frac{1}{1024}
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  3. #3
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    Thank u so much for ur help


    so

    x = 1024

    or

    x = 1/1024
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