Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
- No direct alignment recorded
New NZC (2026)
- No direct alignment recorded
Resources
- Other: Not in the Beta Textbook: logarithms are formally NCEA Level 2 / Year 12 content, so this Year-10 extension LO has no textbook chapter. The proofs are built directly on the Year-10 exponent rules (NZC26-P4-NUM-NSO-K-Y10-04).
- CorbettMaths - Logarithms (the early questions match this LO; the later ones use the log laws to solve equations, which is the sister LO)Questions PDF · Answers
Terminology
- logarithm
- base
- index
- index form
- logarithm form
- power rule
- product rule
- quotient rule
Task goals
- Say what a logarithm asks -- what power of the base gives this number -- and write the definition log_b a = c means b^c = a, with b > 0, b not 1 and a > 0.
- Convert between index form and logarithm form in both directions by holding the base and swapping the index and the answer across the equals sign.
- Evaluate simple logarithms without a calculator by counting up in powers of the base, including log_b 1 = 0, log_b b = 1 and negative answers such as log_10 0.1 = -1.
- Solve an equation holding a single logarithm, such as log_2 x = 5 or log_b 49 = 2, by converting it to index form.
- Prove log_10 10 = 1 and the power, product and quotient log laws from the Year-10 index laws, naming the index law each proof uses.
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.