Advanced · 15 min
Exponentials and logarithms
Model repeated growth and use logarithms to ask for an exponent.
Recognise repeated multiplication
Exponential growth multiplies by a fixed factor at each step. With starting amount A and factor r, the amount after n steps is A × rⁿ.
Worked example
Starting at 10 and doubling three times gives 10 × 2³ = 80.
Read a logarithm as a question
For a positive base other than 1, log base b of a positive number asks which power of b produces that number. It reverses exponentiation.
Worked example
log₂(32) = 5 because 2⁵ = 32.
Compare growth patterns
- List the first four amounts starting at 20 when you add 10 at each step.
- List the first four amounts starting at 20 when you multiply by 1.5 at each step.