Logarithms
Take your work with exponential functions further by learning to solve equations with an unknown exponent.
Counting Days
Log-Exponent Pairs
Inverse of Base 2
Inverse of Exponentiation
Negative Exponents
Fractional Exponents
Evaluating Logarithms
Level Check
Estimating Logs
Graphing Log Functions
Domain of the Logarithm
Fractional Bases
Graphing Fractional Bases
Level Check
The Product Rule
Proving the Product Rule
The Quotient Rule
The Power Rule
Proving the Power Rule
Transforming with Identities
Bases 2, 4 and 8
Bases 2 and 10
Converting Bases
Converting Bases Graphically
Taking Logs of Both Sides
The Unknown Inside a Log
Logs on Both Sides
Solutions and Domains
Using Log Identities
Graphing Solutions
Checking Solutions
Course description
Use graphs and powers you already know to turn exponential questions inside out, building each logarithm rule. By the end of the course, you'll be able to evaluate logarithms in any base, graph them and find their domains, apply the product, quotient, and power rules, convert between bases, and solve equations with an unknown in the exponent or inside a log. You'll also learn to check which answers are valid, since the algebra that solves a log equation can introduce solutions the original equation never had.
Topics covered
- Change of Base
- Checking Solutions
- Domain of the Logarithm
- Estimating Logarithms
- Evaluating Logarithms
- Fractional Bases
- Graphing Log Functions
- Logarithmic Equations
- Logarithms as Inverses
- Power Rule
- Product Rule
- Quotient Rule
Prerequisites and next steps
Before you get started, you should be comfortable with exponential functions and the rules of exponents, since every logarithm rule is proved from an exponent rule. You don't need any prior experience with logarithms to begin, and you won't need a calculator: the course works with bases you can reason about mentally.