Question 3 - A-Level Maths

Edexcel Paper 2 2021 October — Question 3 3 marks

Exam Board	Edexcel
Module	Paper 2 (Paper 2)
Year	2021
Session	October
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Laws of Logarithms
Type	Solve ln equation using subtraction law
Difficulty	Moderate -0.3 This is a straightforward application of logarithm laws (quotient rule) followed by solving a linear equation. The base-3 logarithm adds minimal complexity since students simply apply log laws mechanically then convert to exponential form. Slightly easier than average due to the direct single-technique approach with no conceptual obstacles.
Spec	1.06f Laws of logarithms: addition, subtraction, power rules 1.06g Equations with exponentials: solve a^x = b

Using the laws of logarithms, solve the equation

$$\log _ { 3 } ( 12 y + 5 ) - \log _ { 3 } ( 1 - 3 y ) = 2$$

Show mark scheme Show mark scheme source

Question 3:

Answer	Marks	Guidance
$\log_3(12y+5) - \log_3(1-3y) = 2 \Rightarrow \log_3\frac{12y+5}{1-3y} = 2$	B1/M1 on EPEN	Applies at least one addition or subtraction law of logs correctly. Can also be awarded for using $2 = \log_3 9$
$\log_3\frac{12y+5}{1-3y} = 2 \Rightarrow \frac{12y+5}{1-3y} = 3^2 \Rightarrow 9 - 27y = 12y + 5 \Rightarrow y = \ldots$	M1	Rigorous argument with no incorrect working to remove the log(s) correctly and obtain a correct equation, then solve for $y$
$y = \frac{4}{39}$	A1	Correct exact value. Allow equivalent fractions.

## Question 3:

$\log_3(12y+5) - \log_3(1-3y) = 2 \Rightarrow \log_3\frac{12y+5}{1-3y} = 2$ | B1/M1 on EPEN | Applies at least one addition or subtraction law of logs correctly. Can also be awarded for using $2 = \log_3 9$

$\log_3\frac{12y+5}{1-3y} = 2 \Rightarrow \frac{12y+5}{1-3y} = 3^2 \Rightarrow 9 - 27y = 12y + 5 \Rightarrow y = \ldots$ | M1 | Rigorous argument with no incorrect working to remove the log(s) correctly and obtain a correct equation, then solve for $y$

$y = \frac{4}{39}$ | A1 | Correct exact value. Allow equivalent fractions.

---

Show LaTeX source

\begin{enumerate}
  \item Using the laws of logarithms, solve the equation
\end{enumerate}

$$\log _ { 3 } ( 12 y + 5 ) - \log _ { 3 } ( 1 - 3 y ) = 2$$

\hfill \mbox{\textit{Edexcel Paper 2 2021 Q3 [3]}}

This paper (15 questions)

View full paper

Q1 4 Q2 5 Q3 3 Q4 3 Q5 7 Q6 5 Q7 9 Q8 9 Q9 3 Q10 6 Q11 10 Q12 7 Q13 6 Q14 12 Q15 11

Answer	Marks	Guidance
\(\log_3(12y+5) - \log_3(1-3y) = 2 \Rightarrow \log_3\frac{12y+5}{1-3y} = 2\)	B1/M1 on EPEN	Applies at least one addition or subtraction law of logs correctly. Can also be awarded for using \(2 = \log_3 9\)
\(\log_3\frac{12y+5}{1-3y} = 2 \Rightarrow \frac{12y+5}{1-3y} = 3^2 \Rightarrow 9 - 27y = 12y + 5 \Rightarrow y = \ldots\)	M1	Rigorous argument with no incorrect working to remove the log(s) correctly and obtain a correct equation, then solve for \(y\)
\(y = \frac{4}{39}\)	A1	Correct exact value. Allow equivalent fractions.