# The Power of Logs!

Algebra Level 5

Let $$x,{ x }^{ \log _{ 10 }{ x } },{ y }^{ \log _{ 10 }{ y } },({ xy) }^{ \log _{ 10 }{ (xy) } }\quad$$ be four consecutive terms of a geometric progression. Find the number of ordered pairs $$(x,y)$$ where $$x,y>0$$ which satisfies the above condition.

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