## Problem 2.

Solve the system: $2014 \cdot \lg [x]+\{\lg y\}=2014 \cdot \lg [y]+\{\lg z\}=2014 \cdot \lg [z]+\{\lg x\}=0$.
## Problem 2.

$[x]>0 \Rightarrow x \geq 1$; similarly for the others ......................................................................... 1p

![](https://cdn.mathpix.com/cropped/2024_06_07_7ed169e04a15474689ffg-2.jpg?height=120&width=1366&top_left_y=1542&top_left_x=301)

$\Rightarrow 10^{-\frac{1}{2014}}<[x] \leq 1 \Rightarrow[x]=1 \Rightarrow\{\lg y\}=0 \Rightarrow \lg y \in \mathbb{Z}$; similarly for the others ................... 3p

Thus $x, y, z \in[1,2)$ and for $\lg x=n \in \mathbb{Z} \Rightarrow x=10^{n} \in[1,2) \Rightarrow n=0 \Rightarrow x=1$ $\qquad$