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I have a question regarding logarithm rules.

Could anyone please explain how does equation (3) derived from equation (2)?

I am especially confused regarding the product of $log$ and $exp()$ changed to summation.

Thank you for your help.

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dkssud
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1 Answers1

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This is actually simpler than you think. These are basic properties of $\log$ right $$ \log xy=\log x+\log y\\ \log\frac xy = \log x-\log y $$ Then we also know $\log$ is the inverse function of $\exp$, then we have $$ \log \frac{\exp X}{Z} = \log \exp X-\log Z = -\log Z + X $$

Substitute $Z :=Z(X^n,w) $ $X:=\langle w,\psi(X^n,Y^n)\rangle$ you get what you want.

Binxu Wang 王彬旭
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