In Exercises 81–100, evaluate or simplify each expression without using a calculator. e^ln 125

Key Concepts

Exponential and Logarithmic Functions

Exponential functions involve a constant base raised to a variable exponent, while logarithmic functions are the inverse operations of exponentials. The natural logarithm, denoted as ln, uses the base 'e' (approximately 2.718). Understanding the relationship between these functions is crucial for simplifying expressions like e^ln(x).

Properties of Logarithms

Logarithms have specific properties that simplify calculations, such as ln(a^b) = b*ln(a) and e^(ln(a)) = a. These properties allow us to manipulate logarithmic expressions effectively. Recognizing that e and ln are inverse functions helps in evaluating expressions without a calculator.

Evaluating Expressions

Evaluating expressions involves substituting values and simplifying them according to mathematical rules. In this case, understanding how to apply the properties of logarithms and exponentials allows for straightforward simplification of e^ln(125) to yield the final result. Mastery of this concept is essential for solving similar problems.