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Math Help - x = 25 ^ (1 + log(base 5) x)

  1. #1
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    x = 25 ^ (1 + log(base 5) x)

    Solve for X:

    X = 25 ^ (1 + log(base 5) X)

    My steps:

    Bring the exponent down

    log(base 25) X = 1 + log(base 5) X

    I am stuck here as I have 2 different bases, log X to base 25 and log X to base 5.

    How should I solve this? Thanks.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by shenton View Post
    Solve for X:

    X = 25 ^ (1 + log(base 5) X)

    My steps:

    Bring the exponent down

    log(base 25) X = 1 + log(base 5) X

    I am stuck here as I have 2 different bases, log X to base 25 and log X to base 5.

    How should I solve this? Thanks.
    why did you take log(base25)?

    take log(base5) of both sides:

    log(base5)X = log(base5)25 ^ (1 + log(base 5) X)

    call log(base5) just log, and remember we're working in base 5

    => logx = (1 + logx)log25
    => logx = (1 + logx)2 .................log(base5)25 = 2
    => logx = 2 + 2logx
    => logx = -2
    => 5^-2 = x
    => 1/5^2 = x
    => x = 1/25
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  3. #3
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    Here.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    Here.
    that's a nice way to do it, very elegant. my way was more mechanical and muscle memory based
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