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Math Help - Quadratic involving logarithm problem?

  1. #1
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    Post Quadratic involving logarithm problem?

    Hi all

    I can see here, that

    8n^2 = 64nlog_2n

    can be arranged into  8n^2 - 64nlog_2n = 0 (if I'm correct on that), but I'm just not sure where to go from here.

    If I'm wrong, then I tried diving by 64n on each side to get

     n/8 = log_2n ,

    then applying one of the log laws on each side to get

     2^n^/^8 = 2^l^o^g^_^2^n

    Finally:  2^n^/^8 = n

    Then got stuck here. =(
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  2. #2
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    Quote Originally Posted by RossR View Post
    Hi all

    I can see here, that

    8n^2 = 64nlog_2n

    can be arranged into  8n^2 - 64nlog_2n = 0 (if I'm correct on that), but I'm just not sure where to go from here.

    If I'm wrong, then I tried diving by 64n on each side to get

     n/8 = log_2n ,

    then applying one of the log laws on each side to get

     2^n^/^8 = 2^l^o^g^_^2^n

    Finally:  2^n^/^8 = n

    Then got stuck here. =(
    All your considerations and calculations are OK.

    You can't solve the last equation algebraically. So use a numerical method (for instance Newton) to get an approximate result.

    I've got x = 1.099997030
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  3. #3
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    Thanks! I am interested to know, how you knew this could not be solved algebraically, I guess during your studies numerical methods? Did you study this at university? Is this a topic they went over in your school before uni?
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  4. #4
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    Quote Originally Posted by RossR View Post
    Thanks! I am interested to know, how you knew this could not be solved algebraically, I guess during your studies numerical methods? Did you study this at university? Is this a topic they went over in your school before uni?
    Equations involving functions of mixed type (eg. polynomial and transcendental) can rarely be solved using algebraic methods (unless new functions such as the Lambert W-function are recruited).
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  5. #5
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    Well, not all that "new". The W function was defined by Johann Lambert in the 1760s, about 250 years ago!
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  6. #6
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    Quote Originally Posted by HallsofIvy View Post
    Well, not all that "new". The W function was defined by Johann Lambert in the 1760s, about 250 years ago!
    In terms of the age of much of the mathematics studied by a typical maths student, 250 years ago is quite recent! lol!
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