OCR MEI C3 — Question 5 4 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeExpress y in terms of x (ln/log equations)
DifficultyModerate -0.3 This is a straightforward algebraic manipulation question involving logarithms and square roots. It requires routine application of log laws (bringing down the power, exponentiating both sides) and basic algebraic rearrangement, making it slightly easier than average for C3 level with no problem-solving insight needed.
Spec1.02b Surds: manipulation and rationalising denominators1.06f Laws of logarithms: addition, subtraction, power rules
Make \(x\) the subject of \(t = \ln \sqrt{\frac{5}{(x-3)}}\). [4]
AnswerMarks Guidance
\(t = \ln\sqrt{\frac{5}{(x-3)}} = -\frac{1}{2}\ln\frac{(x-3)}{5}\)M1, M1
\(\Rightarrow -2t = \ln\frac{(x-3)}{5}\)A1
\(\Rightarrow e^{-2t} = \frac{(x-3)}{5} \Rightarrow x = 5e^{-2t} + 3\)A1 Rules of logs; Change to exponentials. 4 marks 
$t = \ln\sqrt{\frac{5}{(x-3)}} = -\frac{1}{2}\ln\frac{(x-3)}{5}$ | M1, M1

$\Rightarrow -2t = \ln\frac{(x-3)}{5}$ | A1

$\Rightarrow e^{-2t} = \frac{(x-3)}{5} \Rightarrow x = 5e^{-2t} + 3$ | A1 | Rules of logs; Change to exponentials. 4 marks

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Make $x$ the subject of $t = \ln \sqrt{\frac{5}{(x-3)}}$. [4]

\hfill \mbox{\textit{OCR MEI C3  Q5 [4]}}
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