logMN

logMN represents the logarithm of the product of two numbers, M and N. In logarithmic notation, it is commonly expressed as log(MN) or log_b(MN), where 'b' is the base of the logarithm. The fundamental property of logarithms states that the logarithm of a product is equal to the sum of the logarithms of the individual factors. This property can be written as log_b(MN) = log_b(M) + log_b(N). This rule is crucial in simplifying logarithmic expressions and solving logarithmic equations. For instance, if you have log(100 * 10), you can rewrite it as log(100) + log(10), which often makes calculations easier. This property holds true for any valid base 'b', which is typically 10 for common logarithms or 'e' (Euler's number) for natural logarithms. Understanding and applying the logMN property is a foundational concept in mathematics, particularly in algebra and calculus, and is used in various scientific and engineering fields.