The product property states that the logarithm of a product is equal to the sum of the logarithms of its factors. In simpler terms, for any positive numbers 'a' and 'b', the relationship can be expressed as: $$\log_b(a \cdot b) = \log_b(a) + \log_b(b)$$. This property is essential in simplifying logarithmic expressions and solving logarithmic equations, making it a fundamental tool in mathematical modeling and analysis.
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