| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2023 |
| Session | October |
| Marks | 8 |
| Topic | Laws of Logarithms |
| Type | Two unrelated log parts: both solve equations |
| Difficulty | Standard +0.3 Part (i) is a routine exponential equation solved by taking logs—standard C2/C3 material. Part (ii) requires applying log laws to combine terms, converting to exponential form, and solving a resulting quadratic equation, which is more involved but still follows a well-practiced procedure with no novel insight required. The 6-mark allocation and 'show detailed reasoning' instruction indicate standard working rather than exceptional difficulty. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
In part (ii) of this question you must show detailed reasoning.
\begin{enumerate}[label=(\roman*)]
\item Use logarithms to solve the equation $8^{2x+1} = 24$, giving your answer to 3 decimal places. [2]
\item Find the values of $y$ such that
$$\log_2(11y - 3) - \log_2 3 - 2\log_2 y = 1, \quad y > \frac{3}{11}$$ [6]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2023 Q6 [8]}}