Exam-style question
Try this first
Which answer avoids the common misconception in the laws of logarithms?.
- A.F4: avoid assuming that logarithm laws apply to products and powers, not arbitrary sums
- B.Use any familiar GCSE calculation even if it ignores the laws of logarithms
- C.Write only the final answer without showing the mathematical method
- D.Change the notation or restrictions to make the algebra look simpler
Model answer
What a good answer should say
- The correct answer is F4: avoid assuming that logarithm laws apply to products and powers, not arbitrary sums.
- This option is best because use inverse relationships, logarithm laws and model assumptions explicitly, then checks that the notation, restrictions and conclusion match the AQA A-level Mathematics objective.
This answer is tied to the objective: F4 Understand and use the laws of logarithms, including log_a x + log_a y = log_a(xy), log_a x - log_a y = log_a(x/y), and k log_a x = log_a(x^k), including cases such as k = -1 and k = -1/2..
Explanation
Why this works
Use the explanation to connect the worked answer back to F4 Understand and use the laws of logarithms, including log_a x + log_a y = log_a(xy), log_a x - log_a y = log_a(x/y), and k log_a x = log_a(x^k), including cases such as k = -1 and k = -1/2..
F4: avoid assuming that logarithm laws apply to products and powers, not arbitrary sums is the correct option. It directly supports the laws of logarithms by requiring the student to use inverse relationships, logarithm laws and model assumptions explicitly.
The other options are weaker because they hide the reasoning, ignore restrictions, or use a generic calculation that may not fit the objective.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: recall.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
No common mistake is linked to this question yet.