| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2023 |
| Session | November |
| Marks | 5 |
| Topic | Laws of Logarithms |
| Type | Solve log equation reducing to quadratic |
| Difficulty | Standard +0.3 This is a straightforward logarithm equation requiring standard manipulation (using log laws to combine terms), converting to exponential form, and solving a resulting quadratic. It's slightly easier than average as it follows a well-practiced procedure with no conceptual surprises, though students must remember the domain restriction x > 2. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
6. Find the values of $x$ such that
$$2 \log _ { 3 } x - \log _ { 3 } ( x - 2 ) = 2$$
\\
\hfill \mbox{\textit{SPS SPS FM Pure 2023 Q6 [5]}}