I have the expression
$$
\frac{\sum_i\ln(x_i)}{p}
$$
where I have $x_1=20$, $x_2 =30$, $x_3=40$ for the $i$th numbers
I was wondering if I continue by $[\ln(20+30+40)]/p$ or if I $[\ln20+\ln30+\ln40]/p$
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3
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3$\begingroup$ Use the latter expression. $\endgroup$– Umberto P.Sep 17, 2013 at 16:28
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$\begingroup$ The $\ln$ is inside the summation. It's the difference between $\sum_i\ln(x_i)$ and $\ln(\sum_i x_i)$. $\endgroup$– StahlSep 17, 2013 at 16:29
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$\begingroup$ thank you so much, is there any particular reason why? I'm sorry if its a simple question I study biology and really should be more apt at maths! Thank you so much again! :) $\endgroup$– Elizabeth SheldonSep 17, 2013 at 16:30
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1 Answer
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If you have $\frac{1}{p}\sum_{i=1}^3 \ln x_i$ that means $\frac{1}{p}(\ln x_1+\ln x_2 + \ln x_3)$. Had you had $\frac{1}{p}\ln \left(\sum_{i=1}^3 x_i\right)$ then that would have been equal to $\frac{1}{p}\ln(x_1+x_2+x_3)$.
