MathsYears 12–13Pure Mathematics

Exponentials and logarithms

Use laws of logarithms; solve exponential equations; model with exponential functions including e^x and ln x

What you'll learn

  1. 1

    Imagine a magic penny that doubles every day. Day 1: 1p, Day 2: 2p, Day 3: 4p — that's exponential growth!

  2. 2

    On day 4, how many pennies do you have? (Hint: double 4p)

  3. 3

    Drag the slider to see how the number of pennies grows on each day. Start at day 1 (1p) and go to day 5.

  4. 4

    We write this as 2³ = 8. The 2 is the base (doubling), the 3 is the exponent (days). The log asks: '2 to what power gives 8?' Answer: log₂8 = 3.

  5. 5

    What is log₂16? (Hint: 2 to what power = 16?)

  6. 6

    Use the slider to find the exponent: 2 to the power of what gives 32?

  7. 7

    If 10³ = 1000, what is log₁₀1000?

Practise Exponentials and logarithms with Whizlo

Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 16–18. Aligned to the UK National Curriculum.