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The function $f(x) = 8 \log_{e} x – x^{2} + 3$ attains its minimum over the interval $[1, e]$ at $x =$____________.

(Here $\log_{e}x$ is the natural logarithm of $x$.)

1. $2$
2. $1$
3. $e$
4. $\frac{1+e}{2}$