# LOG second

Algebra Level 5

$$x_{1} \times x_{2}... \times x_{n}=e$$ and each $$\ln(x_{i})$$ is a proper fraction. Find the greatest integral value of $\ln(x)-\lfloor(\ln x_{1}) \times \ln(x)\rfloor -\lfloor(\ln x_{2}) \times \ln(x)\rfloor -\cdots-\lfloor (\ln x_{n}) \times \ln(x)\rfloor,$

where $$n$$ is the least 2-digit prime number, and $$\ln x$$ is a natural number

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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