| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2021 |
| Session | November |
| Marks | 4 |
| Topic | Laws of Logarithms |
| Type | Two unrelated log/algebra parts - linked parts (hence) |
| Difficulty | Moderate -0.3 Part (i) is trivial logarithm law recall (log a - log b = log(a/b)). Part (ii) requires applying log laws to get y = 3(9-6x) and y/x = 2, then solving the resulting linear system, which is straightforward algebra. This is slightly easier than average due to the routine nature of the techniques, though the simultaneous equations add minor complexity. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}[label=(\roman*)]
\item Write $\log_{16} y - \log_{16} x$ as a single logarithm. [1]
\item Solve the simultaneous equations, giving your answers in an exact form.
$$\log_3 y = \log_3(9 - 6x) + 1$$
$$\log_{16} y - \log_{16} x = \frac{1}{4}$$
[3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2021 Q5 [4]}}