In Exercises 81–100, evaluate or simplify each expression without using a calculator. log 100

Key Concepts

Logarithms

A logarithm is the inverse operation to exponentiation, answering the question: to what exponent must a base be raised to produce a given number? For example, in the expression log_b(a), b is the base, and a is the number for which we want to find the exponent.

Common Logarithm

The common logarithm is a logarithm with base 10, often denoted as log(x) or log_10(x). It is widely used in mathematics and science, particularly for simplifying calculations involving powers of ten, such as log(100) = 2, since 10^2 = 100.

Properties of Logarithms

Logarithms have several key properties that simplify calculations, including the product, quotient, and power rules. For instance, log_b(m*n) = log_b(m) + log_b(n) and log_b(m/n) = log_b(m) - log_b(n). These properties are essential for evaluating and simplifying logarithmic expressions.