MM5: Exponentials, Logarithms and Growth Equations
Official Cambridge & Imperial ESAT specification requirements for Exponentials, Logarithms and Growth Equations on the Mathematics 2 paper. Understand the syllabus boundaries, spot distractor traps engineered by examiners, and master the 2-step Sub-90 shortcuts that compress solve time well below the 88.8-second cutoff.
Official Syllabus Subtopics
Requirements specified in the UAT-UK framework
- 1Laws of logarithms: log(xy) = log x + log y, log(x/y) = log x - log y, log(xᵏ) = k log x
- 2Natural logarithm ln x and base e, change of base formula
- 3Disguised exponential quadratics: a²ˣ + b·aˣ + c = 0 via substitution u = aˣ
- 4Logarithmic inequalities and strict argument domain constraints (x > 0)
- 5Reduction of non-linear power relationships y = a·xᵇ to linear form log y = log a + b log x
Sub-90 Exam Speed Tips
How top candidates solve this spec under the 88.8s clock
Never combine log terms without first verifying that all individual arguments are strictly positive.
For a²ˣ equations, substitute u = aˣ and discard any non-positive roots u ≤ 0.
Examiners engineer distractor options using common algebraic expansions and sign slips. Always test structural ratios or invariants before calculating arithmetic values.
Tested Topics in Specification MM5
Master the individual question patterns and Sub-90 shortcuts for this specification.
Laws of Logarithms, Disguised Exponential Quadratics (a²ˣ + b aˣ + c = 0) & Log Inequalities
Spot disguised quadratics immediately: 4ˣ = (2ˣ)² and 2ˣ⁺ᵏ = 2ᵏ * (2ˣ). By Vieta's formulas, if u₁*u₂ = aˣ¹⁺ˣ² = c/A, then x₁ + x₂ = logₐ(c/A) directly without finding x₁ or x₂!
Ready to Master Specification MM5 Under Exam Conditions?
Practice timed questions under the authentic Pearson VUE interface with live split stopwatch pacing, dry-wipe scratchpad, and distractor forensics.