Overview

Algebra 2

28. CC.HSF.BF.B.5

28.7 Natural log: ln

What Is Natural Log (ln)?

Natural log, written ln, is the logarithm base e. See its definition, formula, graph, and how it connects to exponential functions.

What You'll Learn

The natural log, written ln(x), is the logarithm with base e, where e is approximately 2.71828

ln(x) answers the question: e raised to what power gives x

ln(1) always equals 0, and ln(e) always equals 1

The domain of ln(x) is all positive real numbers, and its graph passes through (1, 0) with a vertical asymptote at x equals 0

ln is sometimes called the Naperian logarithm, and it differs from the common logarithm, which uses base 10

What You'll Practice

Evaluating natural log expressions like ln(e) without a calculator

Simplifying expressions with e raised to natural log powers

Using the inverse relationship between e and ln to solve problems

Why This Matters

Natural logarithms are essential in calculus, physics, and engineering. You'll use ln when studying exponential growth and decay, compound interest, and advanced calculus. Mastering the relationship between e and ln makes complex higher-level math much more manageable.

Before You Start — Make Sure You Can:

Converting from logarithmic form to exponential form Evaluating logarithms without a calculator Common logarithms

This Unit Includes

3 Video lessons

Practice exercises

Learning resources

Skills

Natural Logarithm

Logarithms

Base e

Exponential Form

Inverse Properties

Logarithmic Rules

IL Curriculum Aligned