Exam-style question
Try this first
What is the safest exam approach for the definition of log_a x as the inverse of a^x?.
- A.F3: justify each step using the relevant exponentials and logarithms rule
- B.Use any familiar GCSE calculation even if it ignores the definition of log_a x as the inverse of a^x
- 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 F3: justify each step using the relevant exponentials and logarithms rule.
- This option is best because link the algebraic feature to the corresponding graph feature, then checks that the notation, restrictions and conclusion match the AQA A-level Mathematics objective.
This answer is tied to the objective: F3 Know and use the definition of log_a x as the inverse of a^x, where a is positive and x >= 0; know and use the function ln x and its graph; know and use ln x as the inverse function of e^x..
Explanation
Why this works
Use the explanation to connect the worked answer back to F3 Know and use the definition of log_a x as the inverse of a^x, where a is positive and x >= 0; know and use the function ln x and its graph; know and use ln x as the inverse function of e^x..
F3: justify each step using the relevant exponentials and logarithms rule is the correct option. It directly supports the definition of log_a x as the inverse of a^x by requiring the student to link the algebraic feature to the corresponding graph feature.
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: understanding.
- 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.