Homework Help: Subtraction of Logarithm

1. Jan 6, 2012

HACR

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

2. Relevant equations

log(a/b)=log(a)-log(b)

3. The attempt at a solution

Using the property of log, I came up with $$log(\frac{\lambda-2i\{phi}'(\theta)-\tilde{G}(\theta,\lambda)\lambda}{\lambda-i2{\phi}'(\theta)-\tilde{G_n}(\theta,\lambda)\lambda})$$ but it's not really equal as you can see.

Last edited: Jan 6, 2012