Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the logarithmic function represented as?

1. f(x) = log₀(x)

2. f(x) = b^x

3. f(x) = e^x

4. f(x) = x^b

The correct answer is: f(x) = log₀(x)

The logarithmic function is typically represented as the inverse of an exponential function. Logarithms answer the question: to what exponent must a base be raised to produce a certain number? The function can be expressed as f(x) = log_b(x), where b is the base of the logarithm, and x is the number for which we are finding the logarithm. The choice of f(x) = log₀(x) appears to suggest a base of zero. However, it is important to note that logarithms are defined only for positive real numbers and their bases must be positive numbers other than one. A proper representation of a logarithmic function should adopt a valid base, such as 10 or e (Euler's number), but "log₀" is not mathematically correct in the typical context of logarithms. The representation of logarithmic functions does not include exponential forms, such as f(x) = b^x or f(x) = e^x, nor does it represent power functions like f(x) = x^b. Each of those representations relates to different mathematical concepts, where the first exhibits exponential growth and the latter indicates a polynomial growth pattern. Hence, while the answer provided signifies an intention toward the representation of logarith