Large Logs

Algebra Level 5

If \(x\) is the number of terminating zeroes of \({ 100 }^{ { 1000 }^{ 10000 } }\) and \(y\) is the number of terminating zeroes of \({ 1000 }^{ { 10000 }^{ 100000 } }\), compute \(\left\lfloor \log _{ x }{ y } \right\rfloor\).

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