if x^lox(yz) * y^lox(xz) * z^log(xy) = 2 and x^logx * y^logy * z^logz = 6;then xyz=?

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




Learn how to solve for xyz in the equations x^log(yz) * y^log(xz) * z^log(xy) = 2 and x^logx * y^logy * z^logz = 6. This problem involves key concepts in exponents, logarithms, and algebraic equations, suitable for students in Grades 10-12.

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