# May you log long

Level pending

Let $$x = \log_{10}15$$ and $$y = \log_{10}16$$ and set $$A= \{ \log_{10}1 , \log_{10}2 , \ldots , \log_{10}50 \}$$. Find the number of elements in set $$A$$ that can be written in the form of $$ax+by+c$$, where $$a$$, $$b$$, and $$c$$ are rational numbers.

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