Determine all the numbers $x_1,x_2,x_3,\dots,x_n \gt 0$, for which this equality holds true: $$\sum_{k=1}^{n} |log(x \times x_k)| + \sum_{k=1}^{n} |log(\frac{x}{x_k})|=|\sum_{k=1}^{n} log (x_k)|$$
Your answer should be comma separated values "x1,x2,x3,..."