| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2025 |
| Session | October |
| Marks | 7 |
| Topic | Laws of Logarithms |
| Type | Two unrelated log parts: both solve equations |
| Difficulty | Moderate -0.3 Part (a) is a standard logarithm equation requiring log laws and solving a quadratic, which is routine A-level content. Part (b) is straightforward manipulation of logarithm definition. Both parts are textbook exercises requiring only direct application of learned techniques with no novel problem-solving, making this slightly easier than average but not trivial due to the algebraic manipulation required. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
In this question you must show detailed reasoning. Solutions using calculator technology are not acceptable.
Solve the following equations.
\begin{enumerate}[label=(\alph*)]
\item $2\log_3(x + 1) = 1 + \log_3(x + 7)$ [4]
\item $\log_y\left(\frac{1}{x}\right) = -\frac{3}{2}$ [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2025 Q8 [7]}}