Logs, Rewritten: Working with Different Bases

Logs, Rewritten: Rewriting with Different Bases

Students often learn logarithms as disconnected rules.

Then calculators appear — with only log and ln — and everything feels arbitrary again.

This worksheet brings those pieces together.

Instead of memorizing a “change of base formula,” students are guided to rewrite logarithms using a fixed base, step by step, until the structure becomes clear.

Base 10 and base e are introduced deliberately, used explicitly, and then unified through algebra — so nothing feels magical or optional.

What’s inside

• A short recap of what logarithms mean and how they relate to exponents
• Clear explanations of base 10 and base eee, including why calculators use them
• Worked examples that rewrite logarithms using:
• base 10
• base e
• other fixed bases (e.g. base 2 or 3)
• A fully derived change of base formula (no memorization required)
• A concise summary collecting all logarithm rules used so far
• A focused set of practice questions with explicit instructions about which base to use
• Full, clearly written solutions included at the end

No guessing which method to apply.

No hidden shortcuts.

No rules introduced without explanation.

Just careful rewriting, algebra, and structure.

Who this is for

• IB Mathematics AA SL students
• Learners who understand better when methods are fixed and explicit
• Students confused by calculators showing only log and ln
• Tutors and teachers looking for a clean, concept-first log resource
• Review, intervention, or consolidation before exam-style questions

Approx. time: 25–40 minutes

(depending on pace and discussion)