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Exact logarithms, original domains, complete equations and calibrated models topic check

Practise exact logarithms, original domains, complete equations and calibrated models in G3 Additional Mathematics, check independently, and return later to review. This check covers selected skills, not the whole course topic.

Learning goals
  • Produce exact logarithmic values with valid real bases and arguments
  • Produce a combined logarithm argument with its original domain
  • Produce complete logarithmic equation results and original domains
  • Produce complete real exponential equation results
  • Produce calibrated exponential model parameters, predictions and target times
  • Model and interpret exponential and logarithmic relationships
  • G3 Additional Mathematics 2027
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Produce exact logarithmic values with valid real bases and arguments · Check your progress

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Produce a combined logarithm argument with its original domain · Check your progress

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Produce complete logarithmic equation results and original domains · Check your progress

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Produce complete real exponential equation results · Check your progress

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Produce calibrated exponential model parameters, predictions and target times · Check your progress

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Check again

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Produce exact logarithmic values with valid real bases and arguments · Check again

After practising what your progress check showed, check those skills again.

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Produce a combined logarithm argument with its original domain · Check again

After practising what your progress check showed, check those skills again.

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Produce complete logarithmic equation results and original domains · Check again

After practising what your progress check showed, check those skills again.

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Produce complete real exponential equation results · Check again

After practising what your progress check showed, check those skills again.

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Produce calibrated exponential model parameters, predictions and target times · Check again

After practising what your progress check showed, check those skills again.

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Retention check

Come back later to see whether your learning has lasted.

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Produce exact logarithmic values with valid real bases and arguments · Retention check

Come back later to see whether your learning has lasted.

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Produce a combined logarithm argument with its original domain · Retention check

Come back later to see whether your learning has lasted.

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Produce complete logarithmic equation results and original domains · Retention check

Come back later to see whether your learning has lasted.

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Produce complete real exponential equation results · Retention check

Come back later to see whether your learning has lasted.

Loading your check…

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Produce calibrated exponential model parameters, predictions and target times · Retention check

Come back later to see whether your learning has lasted.

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Practise: Produce exact logarithmic values with valid real bases and arguments

Practise questions on the skills you are learning.

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Practise: Produce a combined logarithm argument with its original domain

Practise questions on the skills you are learning.

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Practise: Produce complete logarithmic equation results and original domains

Practise questions on the skills you are learning.

Loading your check…

Reload the page if the check does not appear.

Practise: Produce complete real exponential equation results

Practise questions on the skills you are learning.

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Practise: Produce calibrated exponential model parameters, predictions and target times

Practise questions on the skills you are learning.

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Revision notes

Revise exponential and logarithmic relationships

Use inverse exponential and logarithmic graphs, retain base and argument restrictions, and solve equations and decay models.

Key ideas

  1. Exponentials, logarithms and domains

    Use inverse graphs, valid bases and original argument conditions to solve exponential equations and interpret a decay model with a fixed background.

  2. Calibrate exponential models from observations

    Match a multiplier to its time step, recover a fixed background from equally spaced readings, and check predictions and attainable target times.

What the syllabus asks

From the G3 Additional Mathematics 2027 syllabus

  • Exponential and logarithmic functions a^x, e^x, log_a x, ln x and their graphs, including laws of logarithms, equivalence of y = a^x and x = log_a y, and change of base of logarithms
  • Simplifying expressions and solving simple equations involving exponential and logarithmic functions
  • Using exponential and logarithmic functions as models