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HSC-ADV · Exponential and Logarithmic Functions

Exponential and Logarithmic Functions

HSC HSC Mathematics Advanced · 2024 content registry · first HSC 2027

Official NSW Curriculum syllabus and implementation timeline ↗Download questions and solutions PDF
E1.1E1.2
Assessment evidence

What these examples cover

These examples show assessable skills, not an official HSC topic weighting or prediction. The 2024 NSW syllabuses have their first HSC examination in 2027; students sitting the 2026 HSC continue under the applicable 2017 syllabus.

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Teacher verification note: check the mathematics, notation, permitted technology and syllabus fit for your cohort before classroom or assessment use.

3 deterministic examples

Exponential and Logarithmic Functions questions with worked solutions

Each question is generated from an existing curriq QDSL archetype at a fixed seed. Marks and catalog content mappings travel with the generated question.

Worked example 1

3 marksadv-e1-1
Logarithmic equation Solve 2lnx=ln(2x+8)2ln x=ln(2x+8).
Part a · 3 marks

Find the admissible solution.

Worked solution

Answer: 1 + sqrt(9)

  1. Logarithm Laws: x^2=2x+c
  2. Solve Quadratic: 4
  3. Domain Check: 1 + sqrt(9)

Catalog reference: adv_nsb20_solve_log_equation · seed 41001

Worked example 2

2 marksadv-e1-1
Mixed-base logarithm equation Solve log(2)x+log(4)x=15log_(2) x+log_(4) x=15.
Part a · 2 marks

Find the exact positive solution.

Worked solution

Answer: 1024

  1. Change Of Base: 10
  2. Solve Logarithmic Equation: 1024

Catalog reference: adv_cssa20_mixed_base_logarithm_equation · seed 41001

Worked example 3

1 markadv-e1-2
Logarithmic domain State the domain of g(x)=ln(x+2pi)g(x)=ln(x+2pi).
Part a · 1 mark

Give the excluded boundary; the domain is all greater values.

Worked solution

Answer: 0 - (2 pi)

  1. Solution Rationale: Result recorded in the checked answer.

Catalog reference: adv_nsb20_log_domain · seed 41001

Content mapping and common errors

Exponential and Logarithmic Functions content identifiers

E1.1

Logarithms and Exponentials

Understand and apply the relationship between exponential and logarithmic functions; use the natural base e.

Common student mistakes
  • ·Incorrect log laws — especially log(a) − log(b) ≠ log(a/b) errors
  • ·Confusing log base 10 with natural log
E1.2

Applications of Exponentials and Logarithms

Model and solve problems involving exponential growth and decay; use logarithms to linearise data.

Common student mistakes
  • ·Using the wrong model (growth instead of decay or vice versa)
  • ·Incorrect linearisation — not taking logs of both sides properly

Source and methodology

Examples are deterministic curriq catalog generations from existing QDSL archetypes at the published fixed seed. The generator copies only student-facing prompts, mark allocations, topic mappings, display tables or options, checked answers and marking-path results into this resource.

Review the official NSW Curriculum source ↗

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