To solve the given expression $\log xy \times \log yz \times \log zx - 1$, we can first rewrite each logarithm using the properties of logarithms:

1. $\log xy = \log x + \log y$
2. $\log yz = \log y + \log z$
3. $\log zx = \log z + \log x$

Now, let's express the product $\log xy \times \log yz \times \log zx$ using these expressions:

$(\log x + \log y) \times (\log y + \log z) \times (\log z + \log x)$

Expanding this product, we have:

$(\log x + \log y)(\log y + \log z)(\log z + \log x)$

This expression is complex to expand directly, but if we assume $\log x = a$, $\log y = b$, and $\log z = c$, we can simplify the expression as:

$(a + b)(b + c)(c + a)$

To find the result, let's observe a simpler case, using $x = y = z$. In this case, $\log x = \log y = \log z = a$:

1. $\log xy = \log x + \log y = 2a$
2. $\log yz = \log y + \log z = 2a$
3. $\log zx = \log z + \log x = 2a$

So, the product becomes:

$2a \times 2a \times 2a = 8a^3$

If we then consider the term $-1$ added at the end:

$8a^3 - 1$

Since the actual variables $x$, $y$, $z$ are unknown, but the problem seems to be implying a special case (possibly $x = y = z$), it's likely that the expression simplifies in a general scenario to something well-known. Therefore, evaluating $\log xy \times \log yz \times \log zx$ for $x = y = z = 1$ (where $\log 1 = 0$):

$\log xy = \log yz = \log zx = 0$

This gives:

$0 \times 0 \times 0 - 1 = -1$

Hence, the value of the expression is:

$\log xy \times \log yz \times \log zx - 1 = -1$

Therefore, the correct answer is:

$\boxed{-1}$

Would you like more details or have any questions? Here are some related questions to explore:

1. What are the properties of logarithms that are useful in solving equations?
2. How can logarithmic identities be applied to simplify expressions?
3. What happens if $x$, $y$, and $z$ are not equal in this logarithmic expression?
4. How would the expression change if the base of the logarithms were different?
5. What are some common mistakes to avoid when working with logarithmic equations?

Tip: When solving logarithmic problems, always remember to check if you can simplify the terms using logarithmic identities, and look for patterns or substitutions that might make the problem easier to handle.