Playbook
Logarithms
33 q · 24% HARD · about 1.6 a paper. The equations page holds 5 of the 8 HARD; the laws and digit counting are cheap.
- Questions in the bank
- 33
- q/paper (21 papers)
- 1.57
- Tagged HARD
- 24%
- Subtopics
- 3
Strand: Selective
When you’ll see it
A logarithm to simplify, a number's digit count, or an equation with logs.
How this chapter is tested
33 questions, about 1.6 a paper, at 24% HARD — and most of that (5 of 8) is the equations page. The laws and digit counting are cheap.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
The laws
log ab = log a + log b, log aⁿ = n log a, log_b a = log a ÷ log b.
Digit counting
A number whose log has characteristic k has k + 1 digits.
Log equations
Combine into one log, then remove it; check every root keeps the arguments positive.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.
log(a + b)
It is not log a + log b.
Roots that break the domain
A root that makes a log's argument negative must be rejected.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each subtopic. Read the notes once, then drill subtopic by subtopic below.
Logarithms notesDrill every Logarithms question
33 questions from the bank, across 3 subtopics.
Drill one subtopic at a time
The 3 subtopics, in teaching order.
- Number of Digits and CharacteristicDrill Number of Digits and Characteristic
- Logarithm Identities and Change of BaseDrill Logarithm Identities and Change of Base
- Solving Logarithmic EquationsDrill Solving Logarithmic Equations
Related playbooks
Often paired with this one — the technique or the trap overlaps. Drill these next.