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 domains *.kastatic.org and *.kasandbox.org are unblocked.

Logarithm properties

14 videos
1 skill
You want to go deeper in your understanding of logarithms. This tutorial does just that by exploring properties of logarithms that will help you manipulate them in entirely new ways (mostly falling out of exponent properties).

Introduction to logarithm properties

VIDEO 9:14 minutes
Introduction to the first two logarithm properties.

Introduction to logarithm properties (part 2)

VIDEO 10:04 minutes
Second part of the introduction to logarithm properties.

Logarithm of a power

VIDEO 4:49 minutes
Logarithm of a Power

Sum of logarithms with same base

VIDEO 5:04 minutes
Sum of Logarithms with Same Base

Using multiple logarithm properties to simplify

VIDEO 2:10 minutes
Using Multiple Logarithm Properties to Simplify

Operations with logarithms


Change of base formula

VIDEO 7:32 minutes
Change of Base Formula

Proof: log a + log b = log ab

VIDEO 7:08 minutes
Proof of the logarithm property: log a + log b = log ab

Proof: a log b = log(b^a), log a - log b = log(a/b)

VIDEO 7:57 minutes
Proofs of the logarithm properties: A(log B) = log (B^A) and log A - log B = log (A/B)

Logarithmic equations

VIDEO 1:27 minutes
Logarithmic Equations

Solving logarithmic equations

VIDEO 4:13 minutes
Solving Logarithmic Equations

Solving logarithmic equations

VIDEO 3:28 minutes
Solving Logarithmic Equations

Logarithmic scale

VIDEO 11:15 minutes
Understanding how logarithmic scale is different from linear scale and why it could be useful

Richter scale

VIDEO 11:19 minutes
The basics of the logarithmic Richter and Moment Magnitude Scales to measure earthquakes