If you're seeing this message, it means we're having trouble loading external resources for Khan Academy.

If you're behind a web filter, please make sure that the domain *.kastatic.org is unblocked.

Math

Algebra II

Conceptual videos and worked examples from basic algebra through algebra 2. Includes videos from the former algebra worked examples playlists.
Community Questions
A thumbnail for: Systems of equations and inequalities
31 8

Systems of equations and inequalities

What happens when we have many variables but also many constraints.
A thumbnail for: Functions and their graphs
61 20

Functions and their graphs

Revisiting what a function is and how we can define and visualize one.
A thumbnail for: Polynomial and rational functions
83 24

Polynomial and rational functions

Exploring quadratics and higher degree polynomials. Also in-depth look at rational functions.
A thumbnail for: Rational expressions
34 23

Rational expressions

You have probably been wondering whether our powers of algebraic problem solving break down if we divide by the variable or we have entire expressions in denominator of a fraction. Well, they don't! In this topic, you'll learn how to interpret and manipulate rational expressions (when you have one algebraic expression divided by another)!
A thumbnail for: Exponential and logarithmic functions
23 6

Exponential and logarithmic functions

An look at exponential and logarithmic functions including many of their properties and graphs.
A thumbnail for: Logarithms
27 4

Logarithms

Log-a-what? No, this tutorial is about neither chopped wood nor music (actually logarithms do have applications in music), but it is fascinating nonetheless. You know how to take an exponent. Now you can think about what exponent you have to raise a number to to get another number. Yes, I agree--unstoppable fun for the whole family. No, seriously, logarithms are used everywhere (including to measure earthquakes and sound).
A thumbnail for: Imaginary and complex numbers
14 7

Imaginary and complex numbers

Understanding and solving equations with imaginary numbers.
A thumbnail for: Conic sections
25 12

Conic sections

A detailed look at shapes that are prevalent in science: conic sections
A thumbnail for: Matrices
36 17

Matrices

Understanding and solving matrices.
Logarithms
Log-a-what? No, this tutorial is about neither chopped wood nor music (actually logarithms do have applications in music), but it is fascinating nonetheless. You know how to take an exponent. Now you can think about what exponent you have to raise a number to to get another number. Yes, I agree--unstoppable fun for the whole family. No, seriously, logarithms are used everywhere (including to measure earthquakes and sound).

Logarithm basics

If you understand how to take an exponent and you're looking to take your mathematical game to a new level, then you've found the right tutorial. Put simply and confusingly, logarithms are inverse operators to exponents (just as subtraction to addition or division to multiplication). As you'll see, taking a logarithm of something tells you what exponent you need to raise a base to to get that number.

Natural logarithms

e is a special number that shows up throughout nature (you will appreciate this more and more as you develop your mathematical understanding). Given this, logarithms with base e have a special name--natural logarithms. In this tutorial, we will learn to evaluate and graph this special function.

Logarithmic scale and patterns

Logarithms show up in science and music far more than you might first imagine. This tutorial explores where these appearances occur!