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Loglog transformation of optimization problem, how can the solution be equal to the nontransformed counterpart?

Consider the following two functions: $$y_t = e^{lt} \cdot e^{st} \cdot \prod_{p=0}^{n} x_{tp}^{b_{tp}}\tag1$$ Where $e^{lt}$ captures the trend, $e^{st}$ captures the seasonality and $x_{tp}$ is our ...
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