In Exercises 21–42, evaluate each expression without using a calculator. log5 (1/5)

Logarithms are the inverse operations of exponentiation. The logarithm of a number is the exponent to which a base must be raised to produce that number. For example, if b^y = x, then log_b(x) = y. Understanding this relationship is crucial for evaluating logarithmic expressions.

The change of base formula allows you to convert logarithms from one base to another. It states that log_b(a) can be expressed as log_k(a) / log_k(b) for any positive k. This is particularly useful when dealing with logarithms of bases that are not easily computable.

Logarithms have several key properties that simplify calculations. For instance, log_b(1) = 0 for any base b, since b^0 = 1. Additionally, log_b(b) = 1, as any number raised to the power of 1 is itself. These properties are essential for evaluating logarithmic expressions without a calculator.