Course: Year 12 Mathematics Advanced

Exponential and Logarithmic Functions

A HSC-focused unit for logarithm laws, change of base, Euler's number, natural logarithms, equations with e and ln, and continuous exponential growth and decay models.

Active lessons

5

Planned lessons

5

Lesson sequence

Learn -> Guided Practice -> Independent Practice -> Mastery Quiz

How to use this unit

  • Check domains before simplifying or solving logarithms.
  • Use multiple-choice exact forms to compare symbolic answers.
  • Isolate exponential terms before applying natural logarithms.
  • Finish with the mixed exam practice lesson.

What this unit covers

Logarithm laws
Change of base
Euler's number e
Natural logarithm identities
Equations with e and ln
Domain restrictions
Continuous growth and decay modelling
Half-life and doubling time

Unit pathway

Lesson pathway

5 of 5 active

1

Lesson 1

Logarithm Laws and Change of Base

Apply product, quotient and power laws, use change of base, evaluate special logarithms, and check logarithm domains.

Active
2

Lesson 2

Euler's Number and the Natural Logarithm

Use e, natural logarithms, inverse identities, and special values such as ln 1, ln e, and ln(e^k).

Active
3

Lesson 3

Solving Equations with e and ln

Solve exponential and logarithmic equations using inverse operations, logarithm laws, exact forms, decimal approximations, and domain checks.

Active
4

Lesson 4

Exponential Growth and Decay Modelling

Use continuous exponential models, interpret parameters, solve for k or t, and handle half-life, doubling time, and contextual units.

Active
5