\[\large{ \lfloor \log_x x! } \rfloor = 11814375113 \]

What is the value of integer \(x\) such that it satisfy the equation above?

**Details and Assumptions**

- \(\lfloor x \rfloor \) is the floor function. ie \(\lfloor 123456.789 \rfloor = 123456 \).

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