MYP · Mathematics (Extended) MYP Year 5

Logarithms

MYP Mathematics Extended, Year 5 — Number & Algebra: Logarithms

24 min readAdvancedCore Number & Algebra strand — recurs across investigation and problem-solving criteria; a near-guaranteed source of at least one multi-part question per assessment.

Every logarithm question is hiding the same command underneath: what power turns this base into that number? Once you can see $lo g_{a} b$ as a disguised exponent, the whole chapter — pH, the Richter scale, compound interest, log graphs — collapses into one repeated move: convert between exponential and logarithmic form, then apply the laws. Exam questions almost never test the definition in isolation; they bury it inside a real formula and expect you to rearrange, simplify, and interpret the result correctly.

Overview — the shape of the chapter

Why logarithms exist

Logarithms are the inverse operation of exponentiation — a 'power finder': $lo g_{a} b$ asks, 'base $a$ , to what power, gives $b$ ?'
Every exponential fact $a^{c} = b$ has an equivalent logarithmic sentence $lo g_{a} b = c$ — these are two names for the same statement, not two separate rules to memorise.
The chapter builds in one direction: definition → laws → change of base → solving equations both ways → graphs → real models. Skipping the definition step is why students start guessing at laws instead of deriving them.

Mind map of Logarithms centred on Logarithms.

Command terms this topic loves to use

Command term	What it demands	AO	Mark-earning move
State / Write down	Give the answer directly with no working shown or required.	AO1 knowledge	Full marks for the correct value alone — but if you show wrong working and only the answer is right, still full marks; if the answer is wrong, working can't rescue it here.
Show that	Prove a given result using explicit, gradable algebraic steps, ending at the stated value.	AO2 application	The final answer is already known to you — every mark comes from the correctness and completeness of the working, not from the number at the end.
Find	Carry out a calculation or solve an equation, with enough working to justify the method.	AO2	Method marks are awarded for correct setup even if arithmetic slips later; a bare correct answer with zero working can still lose marks on multi-step questions.
Justify / Evaluate	State a conclusion (true/false, valid/invalid) AND give the specific reasoning or calculation supporting it.	AO3 reasoning	A correct conclusion with no supporting reasoning typically scores zero — the reasoning IS the mark, not a bonus for it.
Hence	Use the result from the previous part directly, rather than starting a fresh method.	AO2/AO3	An independent alternative method that ignores the earlier part can be capped, even if mathematically correct, when the command is 'hence' rather than 'hence or otherwise'.

Key point

If you can't instantly rewrite

lo g_{a} b = c

a^{c} = b

(and back again), stop and drill that conversion before touching laws or equations — almost every dropped mark in this topic traces back to that one skill being shaky.

Worked example

Command terms in action: state, find, justify

The number of squares in an L-shaped pattern is

S = 3, 5, 7

for figures

n = 1, 2, 3

. (a) Write down

S

for

n = 4

. (b) Find a rule for

S

in terms of

n

. (c) A student claims Figure 50 has 100 squares. Justify whether this is correct.

Overview

Logarithms

Overview — the shape of the chapter

Why logarithms exist

The shape of the chapter

Command terms this topic loves to use