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NSW Curriculum
NSW Education Standards Authority

K–10Mathematics K–10 Syllabus

Record of changes
Implementation for K–2 from 2023 and 3–10 from 2024
Expand for detailed implementation advice

Content

Stage 5

Logarithms (Path)

Stn (Standard), Adv (Advanced) and Ext (Extension) have been used to suggest paths for related Stage 6 courses.

Examine logarithms both numerically and graphically
  • Define the term logarithm: the logarithm of a number to any positive base a is the index to which a is raised to give this number

  • Recognise equivalence where y=ax is equivalent to x=logay where a>0 and a1

  • Translate statements expressing a number in Loading  form into Loading  statements expressing the Loading  of the number

  • Use graphing applications to compare and contrast graphs for the functions y=ax and y=logax

  • Generalise that y=logax is an increasing function when a>1 and decreasing when 0<a<1

Establish and apply the laws of logarithms to solve problems
  • Deduce laws of logarithms from laws of Loading 

  • Establish and use a variety of logarithmic results

  • Apply the laws of logarithms to evaluate and simplify Loading 

  • Solve simple Loading  that involve exponents or logarithms

  • Examine Loading  and explain their use in various contexts

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