We are given two equations involving logarithms and exponents, and the goal is to determine $xyz$. Let's break down and solve each equation step by step.

Equation 1:

$x^{\log_x(yz)} \cdot y^{\log_x(xz)} \cdot z^{\log_x(xy)} = 2$ For each term, we apply the property of logarithms: $a^{\log_a(b)} = b$.

So, the expression simplifies as follows: [ x^{\log_x(yz)} = yz, \quad y^{\log_x(xz)} = (xz)^{\log_x}, \quad z^{\logz reshape as rez in4