Solve each problem. Use a calculator to find an approximation for each logarithm. log 398.4

Key Concepts

Logarithms

A logarithm is the inverse operation to exponentiation, representing the power to which a base must be raised to obtain a given number. For example, in the expression log_b(a) = c, b^c = a. Logarithms are essential for solving equations involving exponential growth or decay and are commonly used in various fields such as science and finance.

Common Logarithm

The common logarithm is a logarithm with base 10, denoted as log(x) or log_10(x). It is widely used in calculations involving large numbers, as it simplifies multiplication and division into addition and subtraction. Understanding how to use a calculator to compute common logarithms is crucial for solving problems that require approximating values.

Calculator Functions

Most scientific calculators have built-in functions for calculating logarithms, typically labeled as 'log' for common logarithms and 'ln' for natural logarithms (base e). Familiarity with these functions allows students to efficiently compute logarithmic values, which is essential for solving problems that involve logarithmic equations or approximations.