prove if x^logyz*y^logxz*z^logxy = 2 and x^logx*y^logy*z^logz = 6 then xyz =?

We are given two equations:

1. \( x^{\log y} \cdot y^{\log x} \cdot z^{\log x} = 2 \)
2. \( x^{\log x} \cdot y^{\log y} \cdot z^{\log z} = 6 \)

We are tasked with finding the value of \( xyz \).

### Step 1: Express both equations using logarithmic identities.

Let's simplify the first equation:

\[
x^{\log y} \cdot y^{\log x} \cdot z^{\log x} = 2
\]

Using the identity \( a^{\log b} = b^{\log a} \), we can rewrite it as:

\[
y^{\log x} \cdot z^{\log x} \cdot x^{\log y} = 2
\]

### Step 2: Simplify the second equation.

For the second equation:

\[
x^{\log x} \cdot y^{\log y} \cdot z^{\log z} = 6
\]

Using the same approach

Prove if x^logy * y^logx * z^logx = 2 and x^logx * y^logy * z^logz = 6, then what is xyz?

This problem involves proving an equation using logarithmic identities and exponential properties. It covers advanced algebra concepts and is ideal for students in Grades 10-12. The solution involves simplifying and solving two logarithmic equations to find the value of xyz.

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