Logarithm Laws and Solving Exponential Equations Using Logarithms

Convert between exponential and logarithmic form and evaluate simple logarithms (e.g. base 10 and base 2) without a calculator.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA6-5
New NZC (2026)
  • NZC26-P4-NUM-NSO-K-Y10-04

Resources

Terminology

  • logarithm
  • log law
  • product law
  • quotient law
  • power law
  • index form
  • logarithmic form
  • base
  • exponent

Task goals

  • Foundation: Convert between exponential and logarithmic form and evaluate simple logarithms (e.g. base 10 and base 2) without a calculator.
  • Proficient: Apply the product, quotient and power laws of logarithms to simplify expressions and solve straightforward exponential equations by taking logarithms of both sides.
  • Excellence: Solve multi-step exponential and logarithmic equations combining several log laws, including equations arising from growth/decay contexts, and justify the validity of solutions.

Where this fits

What leads into this objective, and where it goes next.

Before

Negative and Fractional Indices

Negative and Fractional Indices

Powers & Roots

Powers & Roots

Basic Power Rules

Basic Power Rules

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Logarithm Laws and Solving Exponential Equations Using Logarithms

Logarithm Laws and Solving Exponential Equations Using Logarithms

Next

Year 10 is the last year of this phase — the curriculum lists nothing after this. No extension resources on the site yet.

Also under NA6-5:

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For teachers

Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.