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Math Help - logarithms problem

  1. #1
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    logarithms problem

    log (base a) of 2 = .6055
    log (base a) of 3 = .9597
    log (base a) of 10 = 2.0115

    i need to find the value of log (base a) of 7. the problem is that i can't seem to find any combination of 2, 3 and, 10 multiplied/divided together that would make 7.
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  2. #2
    Senior Member pacman's Avatar
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    see this, Dunham, William - Euler - The Master of Us All - (1999), page 17. It may help

    7 is prime not a factor of 2, 3 and 10.

    That is why you can not use the properties of LOGARITHM to obtain a pattern for base b.

    But it is still solvable, Euler's Formula, log (base b) of 2 = (ln 2)/(ln b)
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  3. #3
    Senior Member pacman's Avatar
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    1. log(base a) 2 = 0.6055

    a^(0.6055) = 2

    a = 2^(1/0.6055) = 3.1416 = pi

    2. log (base a) of 3 = .9597

    a = 3^(1/0.9597) = 3.1416


    Thus, N = log (base a) 7 = log (base pi) 7 = log 7/log pi = log 7/ log 3.1416 = 1.69988 = 1.7
    Last edited by pacman; September 2nd 2009 at 11:58 PM.
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