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The geometric mean of quantities $\{a_1, \dots, a_n\}$ is $$ \bar{a}_g = \left( \prod_{i=1}^n a_i \right)^{1/n} $$ Taking the logarithm of both sides gives $$ \log \bar{a}_g = \frac{1}{n} \sum_{i=1}^n \log a_i $$ so the log of the geometric mean is equal to the arithmetic mean of the logs. In your case, the relevant quantities $a_i$ are the growth rates ...

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