Question 2 - A-Level Maths

Edexcel PMT Mocks — Question 2 4 marks

Exam Board	Edexcel
Module	PMT Mocks (PMT Mocks)
Marks	4
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Exponential Equations & Modelling
Type	Simple exponential equation solving
Difficulty	Moderate -0.8 This is a straightforward exponential equation requiring only basic logarithm manipulation: rewrite base 4 as 2², take logs, and rearrange to match the given form. It's a single-technique question with clear direction about the answer format, making it easier than average but not trivial since it requires understanding of logarithm properties and base conversion.
Spec	1.06f Laws of logarithms: addition, subtraction, power rules 1.06g Equations with exponentials: solve a^x = b

2. Solve $$4 ^ { x - 3 } = 6$$ giving your answer in the form $a + b \log _ { 2 } 3$, where $a$ and $b$ are constants to be found.

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(4 marks)

Answer	Marks
M1	Uses logs in an attempt to solve the equation. Example: takes log base 4 and obtains $(x - 3) = \log_4 6$. Alternatively takes logs (any base) to obtain $(x - 3) \log 4 = \log 6$ and proceeds to $x - 3 = \frac{\log 6}{\log 4}$
A1	Changes log bases to 2 and obtains $(x - 3) = \frac{\log_2 6}{\log_2 4}$
M1	This mark would be awarded for $\frac{\log_2 6}{\log_2 4} = \frac{\log_2(2 \times 3)}{\log_2 2^2} = \frac{\log_2 2 + \log_2 3}{2\log_2 2} = \frac{1 + \log_2 3}{2}$
A1	Correct answer only that leads to a value of x. Example: $x - 3 = \frac{1 + \log_2 3}{2}$ $\Rightarrow x = \frac{7}{2} + \frac{1}{2}\log_2 3$

(4 marks)

**M1** | Uses logs in an attempt to solve the equation. Example: takes log base 4 and obtains $(x - 3) = \log_4 6$. Alternatively takes logs (any base) to obtain $(x - 3) \log 4 = \log 6$ and proceeds to $x - 3 = \frac{\log 6}{\log 4}$

**A1** | Changes log bases to 2 and obtains $(x - 3) = \frac{\log_2 6}{\log_2 4}$

**M1** | This mark would be awarded for $\frac{\log_2 6}{\log_2 4} = \frac{\log_2(2 \times 3)}{\log_2 2^2} = \frac{\log_2 2 + \log_2 3}{2\log_2 2} = \frac{1 + \log_2 3}{2}$

**A1** | Correct answer only that leads to a value of x. Example: $x - 3 = \frac{1 + \log_2 3}{2}$ $\Rightarrow x = \frac{7}{2} + \frac{1}{2}\log_2 3$

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2. Solve

$$4 ^ { x - 3 } = 6$$

giving your answer in the form $a + b \log _ { 2 } 3$, where $a$ and $b$ are constants to be found.\\

\hfill \mbox{\textit{Edexcel PMT Mocks  Q2 [4]}}

This paper (16 questions)

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Q1 5 Q2 4 Q3 3 Q4 6 Q5 6 Q6 9 Q7 5 Q8 5 Q9 5 Q10 6 Q11 4 Q12 6 Q13 6 Q14 9 Q15 9 Q16 12

Answer	Marks
M1	Uses logs in an attempt to solve the equation. Example: takes log base 4 and obtains \((x - 3) = \log_4 6\). Alternatively takes logs (any base) to obtain \((x - 3) \log 4 = \log 6\) and proceeds to \(x - 3 = \frac{\log 6}{\log 4}\)
A1	Changes log bases to 2 and obtains \((x - 3) = \frac{\log_2 6}{\log_2 4}\)
M1	This mark would be awarded for \(\frac{\log_2 6}{\log_2 4} = \frac{\log_2(2 \times 3)}{\log_2 2^2} = \frac{\log_2 2 + \log_2 3}{2\log_2 2} = \frac{1 + \log_2 3}{2}\)
A1	Correct answer only that leads to a value of x. Example: \(x - 3 = \frac{1 + \log_2 3}{2}\) \(\Rightarrow x = \frac{7}{2} + \frac{1}{2}\log_2 3\)