In Exercises 21–42, evaluate each expression without using a calculator. log5 5

Key Concepts

Logarithms

Logarithms are the inverse operations of exponentiation. The logarithm log_b(a) answers the question: 'To what power must the base b be raised to obtain a?' For example, log_5(5) asks what power 5 must be raised to yield 5, which is 1.

Properties of Logarithms

Logarithms have several key properties that simplify calculations. One important property is that log_b(b) = 1 for any base b, since any number raised to the power of 1 equals itself. This property is crucial for evaluating logarithmic expressions quickly.

Base of a Logarithm

The base of a logarithm indicates the number that is raised to a power. In the expression log_5(5), the base is 5. Understanding the base is essential for evaluating logarithmic expressions, as it determines the relationship between the logarithm and its corresponding exponential form.