Let $a_1,a_2,...,a_{10} \in (1, \infty)$ sucht that $\log_a{a_i} \in \mathbb{Q}, \forall i=\overline{1,10}$ ($a=\prod\limits_{i=1}^{10}a_i$). Solve the equation:
$$ \displaystyle \sum\limits_{i=1}^{10}x^{ \log_a{a_i}}=x+9 $$
Equation
For discussing Olympiad Level Algebra (and Inequality) problems
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