| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | October |
| Marks | 8 |
| Topic | Laws of Logarithms |
| Type | Two unrelated log parts: both solve equations |
| Difficulty | Standard +0.3 Part (a) is a straightforward logarithm definition question requiring simple algebraic manipulation (x² = 64). Part (b) involves standard log laws (combining logs, converting to exponential form) and solving a quadratic, but follows a routine procedure without requiring novel insight. Slightly above average difficulty due to the multi-step algebraic manipulation in part (b) and potential for algebraic errors, but still a standard textbook exercise. |
| Spec | 1.06c Logarithm definition: log_a(x) as inverse of a^x1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}[label=(\alph*)]
\item Find the positive value of $x$ such that
$$\log_x 64 = 2$$ [2]
\item Solve for $x$
$$\log_2(11 - 6x) = 2\log_2(x - 1) + 3$$ [6]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2022 Q4 [8]}}