| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2026 |
| Session | November |
| Marks | 5 |
| Topic | Laws of Logarithms |
| Type | Solve log equation with domain restrictions |
| Difficulty | Standard +0.3 This is a straightforward logarithm equation requiring standard manipulation: combining logs using laws (2log₃x = log₃x²), forming a single logarithm, converting to exponential form, and solving the resulting quadratic. It's slightly easier than average as it follows a predictable template with no conceptual surprises, though students must remember to check validity of solutions in the original logarithmic domain. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
Find the values of $x$ such that
$$2\log_3 x - \log_3(x - 2) = 2$$
[5]
\hfill \mbox{\textit{SPS SPS FM 2026 Q6 [5]}}