Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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Which property applies to the statement logb(M/N)?

logb(M) + logb(N)
logb(M) - logb(N)
logb(M) × logb(N)
logb(M^p) = logb(M) + p

The correct answer is: logb(M) - logb(N)

The statement logb(M/N) represents the logarithm of a quotient. In logarithmic terms, the property that applies here is that the logarithm of a division can be expressed as the difference of the logarithms of the numbers involved. Specifically, logb(M/N) can be rewritten as logb(M) - logb(N). This property is derived from the definition of logarithms and the laws that govern their operations, which state that dividing two numbers is equivalent to finding the logarithm of the numerator and subtracting the logarithm of the denominator. Understanding this property is essential in logarithmic calculations, as it allows for simplification and transformation of expressions involving logarithms. By using this property, one can facilitate easier manipulation of logarithmic expressions, particularly in solving equations or evaluating logarithmic functions. Hence, the correct choice is the one that denotes the relationship between the logarithm of a quotient and the difference of the logarithms.