Mr. Integral

THE BIG IDEA

Logarithms

How long does repeated growth take?

Exponents describe repeated multiplication. Logarithms reverse the question: which exponent produces a target? Keeping that inverse relationship in view makes the algebraic rules less arbitrary.

Begin the first lesson →See the lesson route ↓

15 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Exponential growth
  2. asking for the exponent defines02Logarithms
  3. multiplying growth factors explains03Combining logs
  4. comparing scales leads to04Change of base

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Exponential Functions2 lessons
  1. 01Defining the Exponential FunctionDistinguish repeated multiplication from repeated addition.
  2. 02Graphing Exponential FunctionsRead growth, decay and asymptotes from an exponential graph.
Definition and Basic Concepts4 lessons
  1. 03Defining the LogarithmTranslate a logarithm into an exponential equation.
  2. 04The Inverse of an Exponential FunctionConnect exponential growth with its logarithmic inverse.
  3. 05The Inverse of a Logarithmic FunctionRecover an exponential function from a logarithm.
  4. 06Conditions on the Base and the ArgumentCheck base and argument restrictions before applying log rules.
The Rules8 lessons
  1. 07The Four Basic RulesUse the basic inverse identities of exponents and logarithms.
  2. 08When the Base Is Not WrittenIdentify a logarithm’s base from the stated convention.
  3. 09The Natural LogarithmUse natural logarithms to undo exponentials with base e.
  4. 10The Product RuleCombine sums of logarithms using the product rule.
  5. 11The Quotient RuleCombine differences of logarithms using the quotient rule.
  6. 12Swapping the Base and the ExponentExplain why a base and logarithmic exponent can exchange roles.
  7. 13When a Logarithm Is the ExponentSimplify exponentials containing a matching logarithm.
  8. 14Changing the BaseChange a logarithm to a convenient base.
Graphing Logarithmic Functions1 lessons
  1. 15Graphing Logarithmic FunctionsConnect a logarithm’s domain to shifts and asymptotes.