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Yes. More generally, suppose you know the size of the group $\mathbb{G}$ you are working in (RSA, class group etc). Let $A = g^n$ where $n$ is the product of the elements in the committed set. Assuming $n$ is co-prime to $|\mathbb{G}|$, you can compute integers $a_1$, $a_2$ such that $$a_1 x + a_2 n \equiv 1 \pmod{|\mathbb{G}|}\;\;,\;\; |a_2| < |x|.$$ ...

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