Suppose `x;y;zgt0` and are not equal to 1 and `log x+log y+log z=0`. Find the value of `x^(1/log y+1/log z)xx y^(1/log z+1/log x)xx z^(1/logx+1/logy)` (base 10)

Explanation

To solve the problem, we need to find the value of the expression \( x^{\frac{1}{\log y} + \frac{1}{\log z}} \cdot y^{\frac{1}{\log z} + \frac{1}{\log x}} \cdot z^{\frac{1}{\log x} + \frac{1}{\log y}} \) given that \( \log x + \log y + \log z = 0 \).

### Step-by-step Solution:

1. **Use the Given Condition**:
We know that:
\[
\log x + \log y + \log z = 0
...