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How to Mark A-level Logs & Exponentials by the Mark Scheme

Logarithm and exponential questions reward two things the mark scheme separates carefully: applying the log laws correctly (method) and giving the answer in the required form (accuracy). Students who can do the algebra still lose marks on the last line. Here's how examiners award them.

Solving an exponential equation

For solve 3^x = 20, a typical mark scheme:

• M1 — taking logs of both sides (any base) and using the power law: x log 3 = log 20.
• A1 — correct exact form x = log 20 / log 3 (or ln equivalent).
• A1 — correct value to the required accuracy (e.g. 3 s.f.), if asked.

The method mark is for the log step, not the final number — show it and you bank the M1 even if the arithmetic slips.

Using the log laws

Questions like "express as a single logarithm" award the M for correct use of log a + log b = log ab, log a − log b = log(a/b), n log a = log aⁿ. The A mark needs the fully simplified, correct result. The classic loss: combining the laws but slipping a sign or a coefficient — M1 holds, A1 goes.

The marks students lose most

1. Decimal where exact was required

"Give your answer in exact form" + a rounded decimal = lost accuracy mark (often a cao demand).

2. Misapplying the power law

Writing log(x²) = (log x)² is the classic error — the method mark is lost because the law is wrong, which then blocks the answer mark.

3. Domain slips

Accepting a "solution" that makes a log of a negative — examiners deduct the accuracy mark for the invalid root.

Marking it the examiner's way

Award the M for the log/exponential step being correct, the A only when the final form matches what was asked (exact vs decimal, single log, valid domain). Point the student to the specific law or the form — "your method's right, but they wanted exact form" wins back the easiest marks.