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Subtraction of Logarithm

  1. Jan 6, 2012 #1
    1. The problem statement, all variables and given/known data
    If [tex]\tilde{G_n}(\theta,\lambda)= \sum_{k=1}^{n} \tilde{g_(k,1)}(i\lambda)\frac\{{theta}^{k}}{k!}[/tex], show that [tex]log(1-\frac{\tilde{G}(\theta,\lambda)\lambda}{\lambda-i2{\phi}'(\theta)})-log(1-\frac{\tilde{G}_n(\theta,\lambda)\lambda}{\lambda-i2{\phi}'(\theta)})=log(1-\frac{\lambda}{\lambda-i2{\phi}'(\theta)}\frac{\tilde{G_n}(\theta,\lambda)-\tilde{G}(\theta,\lambda)}{1-\tilde{G_n}(\theta,\lambda)\lambda(\lambda-2i\phi'(\theta))^{-1}})[/tex]

    2. Relevant equations


    3. The attempt at a solution

    Using the property of log, I came up with [tex]log(\frac{\lambda-2i\{phi}'(\theta)-\tilde{G}(\theta,\lambda)\lambda}{\lambda-i2{\phi}'(\theta)-\tilde{G_n}(\theta,\lambda)\lambda})[/tex] but it's not really equal as you can see.
    Last edited: Jan 6, 2012
  2. jcsd
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