A-level · Beta
Exponentials and logarithms
Explore growth, decay, asymptotes and inverse graphs.
Drag T to translate the graph; drag Q to trace a valid input.
Tab to a handle, then use the arrow keys. Use the sliders for precise values.
The exponential has horizontal asymptote y = 0.
- Trace Q (approx.)
Base e is approximately 2.71828. Logarithms and inverse graphs are drawn only on their valid domains; numerical outputs are rounded to 4 places.
Predict, test and explain
Step 1 of 3
Predict
What is ln(e²)?
Explore and compare
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Try it in the simulation. Change one thing at a time.
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Hints, self-check and connections
Try a self-check
Fixed values, separate from the diagram controls.
What is ln(e²)?
Hint
A logarithm asks which exponent produces its input.
Reveal answer
The logarithm undoes the exponential and returns its exponent.
Build an explanation
Hint 1
A logarithm asks which exponent produces its input.
Hint 2
An exponential and its logarithm are inverse functions.
Hint 3
For a transformed logarithm, check that its actual argument is positive.
Worked example
This example uses fixed values, separate from the diagram controls.
Solve 2ˣ = 8.
- Write 8 as 2³.
- The equal positive bases have equal exponents.
- Therefore x = 3.
Answer: x = 3.
Connect this idea
Watch out: The logarithm returns the exponent, not the original exponential value.
Specification and learning route
AQA F1, F3, F5 · Edexcel Pure 6.1, Pure 6.3, Pure 6.5
AS and A-level. This model illustrates selected content; references are not a claim of full coverage or exam-board endorsement.
Useful starting knowledge: Indices; Algebraic equations; Functions and graphs.