Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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Which of the following is a rule of logarithms?

logb(1) = 1
logb(b) = 0
logb(MN) = logb(M) - logb(N)
logb(b^p) = p

The correct answer is: logb(b^p) = p

The statement that is correct is based on a fundamental property of logarithms. The logarithmic identity states that the logarithm of a base raised to an exponent is equal to the exponent itself. Specifically, for any base $ b $ (where $ b > 0 $ and $ b \neq 1 $) and any exponent $ p $, the expression $ \log_b(b^p) $ evaluates to $ p $. This reflects the inverse relationship between exponentials and logarithms. When you take the log of a number that is itself an exponentiation of the base, you effectively reverse the operation, leading you back to the exponent, which is why this property holds true. This property is crucial in many aspects of mathematics, especially in solving equations involving exponential growth, and in simplifying complicated logarithmic expressions. It also underscores the foundational role that logarithms play in relating multiplication (exponents) to addition (logs), helping to illustrate their usefulness in various mathematical contexts. While the other statements may involve logarithmic concepts, they contain inaccuracies regarding the fundamental rules of logarithms.