Exponentials and logarithms · Year 12
In Year 12 you learn: exponentials and logarithms.
Exponentials like 2ˣ and eˣ model growth and decay: populations, savings, radioactivity, cooling. Logarithms are their inverse — log₂ 8 = 3 because 2³ = 8 — and they let you solve equations where the unknown is in the power.
Key facts
- aˣ = b means the same as logₐ b = x.
- logₐ a = 1 and logₐ 1 = 0.
- ln x is the logarithm to base e (about 2.718): ln(eˣ) = x and e^(ln x) = x.
- In y = Ae^(kt), k > 0 means growth and k < 0 means decay.