If lim⁡n→∞n⋅3nn⋅(x−1)n+n⋅3n+1−3n=13\lim_{n \to \infty} \frac{n \cdot 3^n}{n \cdot (x-1)^n + n \cdot 3^{n+1} - 3^n} = \frac{1}{3}…

Problem

If lim⁡n→∞n⋅3nn⋅(x−1)n+n⋅3n+1−3n=13\lim_{n \to \infty} \frac{n \cdot 3^n}{n \cdot (x-1)^n + n \cdot 3^{n+1} - 3^n} = \frac{1}{3} , the number of the integral values of xx is .....

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