---
title: Logarithms
description: Logarithms are the inverse operations of exponentiation, representing the power to which a base must be raised to yield a given number. Learners will understand logarithmic properties, change of base formulas, and how to solve logarithmic equations.
category: mathematics
subcategory: algebra
difficulty: beginner, intermediate, advanced
url: /subject/logarithms
---

# Logarithms

Logarithms are the inverse operations of exponentiation, representing the power to which a base must be raised to yield a given number. Learners will understand logarithmic properties, change of base formulas, and how to solve logarithmic equations.

## Available Resources

1 Books • 3 Courses • 3 Websites

## Websites

### 1. Art of Problem Solving: Logarithms

Art of Problem Solving wiki article defining logarithms and their core identities, including product, quotient, power and change-of-base rules, with competition-style practice problems. Learners apply log properties to the kind of problems found on AMC and AIME contests.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://artofproblemsolving.com/wiki/index.php/Logarithms

**Tags:** logarithms, log-properties, competition-math, algebra

### 2. Purplemath: Logarithms

Purplemath lesson introducing logarithms as the inverse of exponentials, converting between exponential and log form, evaluating simple logs, and using common and natural logs. Learners gain fluency with log notation before tackling log rules and equations in later pages.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://www.purplemath.com/modules/logs.htm

**Tags:** logarithms, exponential-functions, algebra, log-notation

### 3. mathsisfun.com

MathIsFun.com is a beginner-friendly math site that explains concepts with clear, step-by-step lessons and interactive activities. It covers topics from algebra and linear equations to geometry, fractions, data, and more, with practice problems, worksheets, and quizzes.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathsisfun.com

**Tags:** websites, mathematics-statistics, algebra

## Courses

### 1. Logarithms and Logarithmic Functions

Master logarithms & logarithmic functions with this free course by Sal Khan! Understand logs, solve equations, & explore their applications.

**Difficulty:** Intermediate | **Price:** Free

**Link:** https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs

**Tags:** logarithms, logarithmic-functions, exponential-equations, algebra-2

### 2. Introducción al cálculo

**Author:** Jaume Pujol, Mercè Villanueva

Spanish-language course from the Universitat Autònoma de Barcelona that reviews numbers and functions, polynomial, exponential, logarithmic and trigonometric functions, then introduces differentiation, integration and complex numbers. Prepares students for a first-semester university calculus course in science or engineering.

**Difficulty:** Beginner | **Language:** English | **Duration:** 6-8 horas de trabajo por módulo | **Price:** Free

**Link:** https://www.coursera.org/learn/introduccion-al-calculo

**Tags:** precalculus, functions, trigonometry, differentiation, integration, spanish-language

### 3. Algebra: Elementary to Advanced - Polynomials and Roots

**Author:** Joseph W. Cutrone

Third course in Johns Hopkins's algebra sequence, covering exponential functions, polynomial arithmetic and factoring, square and nth roots, and percent and interest applications. Finishes with a cumulative exam, preparing you for precalculus, statistics or data science coursework.

**Difficulty:** Beginner | **Language:** English | **Price:** Free

**Link:** https://www.coursera.org/learn/polynomials-roots

**Tags:** polynomials, factoring, exponents, radicals, algebra

## Books

### 1. Precalculus

**Author:** Ron Larson, Robert P. Hostetler, Bruce H. Edwards

A graphing-calculator-based precalculus textbook covering functions, polynomial and rational functions, exponential and logarithmic functions, trigonometry, and analytic geometry, with worked examples and extensive exercise sets that prepare students to handle the algebra and function analysis required in calculus.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/0618394664?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, algebra

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