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Math Help - Solving for log

  1. #1
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    Solving for log

    Problem: If log(base a)5 = x and log (base a)7 = y, then log (base a) 1.4^(1/2) =?

    The answer is 1/2 x (y-x)

    (I hope you follow my notation) Thanks!
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  2. #2
    Super Member Quacky's Avatar
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    Re: Solving for log

    We have \log_a(5) and \log_a(7) and a target of \log_a(1.4^{0.5})

    Seems easiest to work backwards.

    \log_a(1.4^{0.5})

    =\frac{1}{2}\log_a(1.4) as \log(x^n)=n\log{x}

    The task becomes getting \log_a(1.4) in terms of \log_a(5) and \log_a(7)

    Best approach?

    Well, \log_a(1.4)=\log_a(\frac{2\times{7}}{10})

    =\log_a(\frac{7}{5})

    Think about your log laws here.
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  3. #3
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    Re: Solving for log

    I used the subtraction rule to get 1/2(y-x)
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