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As part of some self study I need to calculate the Cramer Rao Lower Bound. In some textbook and articles I see Log used and in others I see Ln used. Does it matter which I use as long as I am consistent in usage?

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Standard convention for writing $\log_e x$ is $\ln x$. Some authors use $\log$ in stead of $\ln$. But in that case, the meaning is well conveyed either in the proof or in the beginning of the text where the author defines notations. In general $\ln x=2.303\log x$.

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