| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2024 |
| Session | October |
| Marks | 6 |
| Topic | Laws of Logarithms |
| Type | Identify errors in student work |
| Difficulty | Moderate -0.3 Part (a) requires identifying algebraic errors (squaring vs multiplication, missing a solution), which is straightforward pattern-spotting. Part (b) is a standard quadratic-in-disguise problem requiring substitution and solving, then converting back using logarithm laws. This is routine A-level technique with no novel insight required, making it slightly easier than average. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
A student was asked to solve the equation $2(\log_3 x)^2 - 3 \log_3 x - 2 = 0$. The student's attempt is written out below.
$2(\log_3 x)^2 - 3 \log_3 x - 2 = 0$
$4\log_3 x - 3 \log_3 x - 2 = 0$
$\log_3 x - 2 = 0$
$\log_3 x = 2$
$x = 8$
\begin{enumerate}[label=(\alph*)]
\item Identify the two mistakes that the student has made. [2]
\item Solve the equation $2(\log_3 x)^2 - 3 \log_3 x - 2 = 0$, giving your answers in an exact form. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2024 Q7 [6]}}