Logarithmic functions.
Understand logarithms as inverse functions, solve equations, sketch graphs and use logarithmic derivatives and models with valid domains.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Exponential/logarithmic inverse relationship
Read logarithms as exponents and use inverse functions with their correct domains.
- 02
Logarithm laws and change of base
Combine and separate logarithms safely, then calculate unfamiliar bases.
- 03
Solving exponential equations
Solve exponential equations exactly with logarithms and interpret solutions in context.
- 04
Natural logarithms
Use the natural logarithm as the inverse of the natural exponential function.
- 05
Logarithmic graphs, domains and transformations
Sketch transformed logarithms using domains, asymptotes and selected exact points.
- 06
Differentiating logarithms and composite logarithms
Differentiate logarithmic expressions while retaining their original domains.
- 07
Logarithmic modelling
Build and interpret logarithmic models with realistic domains, units and limitations.
Topic review
Revisit the key ideas, then choose a practice paper.