To expand \(\log(x^{25}y)\) fully using the logarithmic rules, let's apply the Product Rule and the Power Rule.
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Using the Product Rule: \[ \log(x^{25}y) = \log(x^{25}) + \log(y) \]
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Using the Power Rule for the first term: \[ \log(x^{25}) = 25\log(x) \]
Combining these, we get: \[ \log(x^{25}y) = 25\log(x) + \log(y) \]
However, it seems we need to express it in terms of subtraction and handle any constants. We can write it as: \[ 25\log(x) + \log(y) \]
But none of the provided responses include \(25\log(x) + \log(y)\) directly. If it were asked to keep it in terms of simpler expressions, we might see something else in the options:
None of the options are exactly the answer derived above, but they seem to have interpretations based on similar expressions. The closest option related to logarithm terms might indicate simplifying or focusing on values.
However, in contextual reference based on your wording of responses, the \(2\log(x) - \log(5y)\) appears off.
But if we were aligning true straightly with outlined properties you'd have:
\[ \text{None directly match, but correct is } 25\log(x) + \log(y). \]
In conclusion, let's check final values of queries. Of the offered options, the accurate full expansion doesn't fit. Please adjust options or specify more precise terms expected in collapse of definitions regarding prefacing logs.
In any typical base format at above evaluated further:
\(\text{However, the correct logarithmic expression should be articulated: } 25\log(x) + \log(y).\)