- #1

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## Homework Statement

Prove the following statement:

[tex] ln|1+\sigma x | = \frac{1}{2} ln|1-x^2| + \frac{\sigma}{2} ln| \frac{ |1+x|}{|1-x|}

[/tex]

## Homework Equations

## The Attempt at a Solution

Starting from right to left would be easier:

[tex]

= \frac{1}{2} ln|(1+x)(1-x)| + \frac{\sigma}{2} ln| 1+x| - \frac{\sigma}{2} ln(1-x) \\

= \frac{1}{2} [ ln(1+x) + ln(1-x) + \sigma ln(1+x) - \sigma ln(1-x)] \\

=\frac{1}{2} [ln|(1+x)(1+\sigma)| + ln|(1-x)(1-\sigma)|] \\

= \frac{1}{2} [ ln |(1+x)^{1+\sigma} (1-x)^{1-\sigma} |]\\

= \frac{1}{2} ln |( 1+x ) (1+x)^\sigma \frac{1+x}{(1-x)^\sigma}|]

[/tex]

Then I get stuck. Does anyone know what I'm missing?