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## Main Question or Discussion Point

I have a problem taking the log of this expression [tex]\prod_{i=1}^m[\frac{1}{\sqrt{2\pi v}}\exp{(\frac{-u_{i}^2}{2v_{i}})}][/tex]

Now I would get [tex]\ln({\frac{1}{\sqrt{2\pi v}}})(\sum_{i=1}^m{\frac{-u_{i}^2}{v_{i}}})[/tex]

The author gets, by ignoring the constant multiplicative factors, [tex]\sum_{i=1}^m (-\ln{v_{i}}-\frac{u_{i}^2}{v_{i}})[/tex]

Can anybody tell me where the [itex]\ln{v_{i}}[/itex] comes from and what I have done wrong?

Now I would get [tex]\ln({\frac{1}{\sqrt{2\pi v}}})(\sum_{i=1}^m{\frac{-u_{i}^2}{v_{i}}})[/tex]

The author gets, by ignoring the constant multiplicative factors, [tex]\sum_{i=1}^m (-\ln{v_{i}}-\frac{u_{i}^2}{v_{i}})[/tex]

Can anybody tell me where the [itex]\ln{v_{i}}[/itex] comes from and what I have done wrong?