Pre-U Pre-U 9794/2 2012 June — Question 4 4 marks

Exam BoardPre-U
ModulePre-U 9794/2 (Pre-U Mathematics Paper 2)
Year2012
SessionJune
Marks4
TopicExponential Equations & Modelling
TypeSimple exponential equation solving
DifficultyEasy -1.2 This is a straightforward logarithmic equation requiring only the standard technique of taking logs of both sides and applying log laws to isolate x. It's a routine textbook exercise with a single clear method and no problem-solving required, making it easier than average but not trivial since students must execute the algebraic manipulation correctly.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b
Use logarithms to solve the equation \(2^{2x-1} = 5\). [4]
AnswerMarks Guidance
Take logarithms and apply log rule: \((2x - 1)\log 2 = \log 5\)M1, A1, M1 Up to 1 error
Rearrange to make \(x\) the subject
Obtain \(x = \frac{\log 5}{\log 4} = 1.66096...\) AEFA1 [4] [4] 
Take logarithms and apply log rule: $(2x - 1)\log 2 = \log 5$ | M1, A1, M1 | Up to 1 error

Rearrange to make $x$ the subject | 

Obtain $x = \frac{\log 5}{\log 4} = 1.66096...$ AEF | A1 [4] | [4]
Use logarithms to solve the equation $2^{2x-1} = 5$. [4]

\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2012 Q4 [4]}}
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