The definition of a logarithm, the laws of logarithms, simplifying expressions, solving logarithmic equations and equations of the form aˣ = b.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
A logarithm is just an exponent in disguise. Master the three laws and you can undo any power.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
See y = log x as the reflection of y = a^x in y = x.
Copy these into your notebook in your own words — that is how they stick.
log_a b = c ⇔ aᶜ = b (a > 0, a ≠ 1, b > 0).
log_a 1 = 0; log_a a = 1.
log_a(PQ) = log_a P + log_a Q.
log_a(P/Q) = log_a P − log_a Q.
log_a(Pᵇ) = b log_a P.
Combine to a single log, convert to index form, solve, reject arguments ≤ 0.
x log a = log b → x = log b / log a.
log(P + Q) ≠ log P + log Q; log P / log Q ≠ log(P/Q).
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Additional Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (27 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [15 marks]
Answer all parts.
(a) Write 2 log₅ x + 2 − log₅ y as a single logarithm. [3]
(b) Solve log₃(x + 2) + log₃(x − 4) = 3. [5]
(c) Solve 5^(2x−1) = 40, giving x to 2 decimal places. [4]
(d) Given log₂ x = 6 and log₂ y = 4, find log₂(x²/y). [3]
Question 2 [12 marks]
Answer all parts.
(a) Solve log_a(2x + 5) − log_a(3x − 10) = log_a(x − 14), stating clearly why one root is rejected. [6]
(b) Show that log₂ 40 − log₂ 5 = 3. [3]
(c) Express log_a(a²/√b) in terms of log_a b. [3]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.