If `log_(theta)x-log_(theta)y= a, log_(theta)y-log_(theta)z=b` and `log_(theta)z- log_(theta)x=c`, then find the value of `(x/y)^(b-c) x(y/z)^(c-a)x(z/x)^(a-b)`

Explanation

To solve the problem, we start with the given equations:

1. \( \log_{\theta} x - \log_{\theta} y = a \)
2. \( \log_{\theta} y - \log_{\theta} z = b \)
3. \( \log_{\theta} z - \log_{\theta} x = c \)

We need to find the value of the expression:

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