Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What is the base for common logarithms?

2
e
10
Any positive number

The correct answer is: 10

The base for common logarithms is 10. Common logarithms are typically denoted as log(x) without indicating a base or with a subscript indicating the base, such as log₁₀(x). This means that when you see log(x), it is understood to refer to log base 10. This is particularly useful in many practical applications, especially in science and engineering, where calculations often involve powers of ten. The use of a base of 10 allows for easier understanding and communication of large scale numbers, as it aligns with the decimal system most commonly used. Understanding that the common logarithm is based on 10 is essential when solving exponential equations or when you need to convert between exponential and logarithmic forms. Recognizing this base helps in simplifying and solving logarithmic expressions, especially in calculations involving multiplication and division.